Hypothesis: She never existed, nor did her 'castle', in this exact name and location at least.

This autobiography is not always a reliable historical source for either persons, locations or events.

It is certain that Bergman used some real-life persons and real-life names for them alongside with pseudonyms for others in his autobiography. A few of these pseudonyms can be revealed, some not. The name 'von Merkens' appears to be a pseudonym, and one that is used for an almagamation instead of a direct shift in identity. As such the search for the 'von Merkens' castle' may be wrong headed.

Original text in Bergman's autobiography

The quote in question reads typo-corrected and in context:

She realized now that she loved him without reservations, so cast aside all conventions and not only became the quartet’s administrator and manager, but also managed her husband’s love affairs with firmness and humour. She made friends with his mistresses, supervised the erotic traffic like a station-master, and became her husband’s confidante. He did not stop lying, because he was incapable of telling the truth, but he no longer had to camouflage his lechery. With determination and a talent for organization, Andrea piloted her musicians through endless tours, both at home and abroad. Every summer during the inter-war period, they were invited to stay at a schloss near Stuttgart. This castle lay in beautiful countryside with wide vistas over mountains and rivers. Its chatelaine was a somewhat eccentric elderly lady called Mathilde von Merkens, the widow of an industrial magnate. Both she and the schloss had decayed.

Despite this, she went on year after year, bringing together some of Europe’s most distinguished musicians, including Casals, Rubinstein, Fischer, Kreisler, Furtwangler, Menuhin and Vogler. Every summer, they obeyed the call, ate at her widely praised table, drank her fine wines, covered their own and other men’s wives and made great music.

Andrea still retained her talent for vulgar Italian story telling. She had a hearty laugh. Her mad, bizarre, obscene and comical stories were material that positively demanded a film. I decided to make a comedy of it all.

Unfortunately I missed the point, a fact I realized only when the film had been irretrievably made.

Andrea came to see Ka’bi and me in Djursholm, bringing with her some photographs from a summer at Mathilde von Merken’s schloss, among them a picture that made me wail with misery. The picture is of the company on the terrace after what has clearly been a splendid dinner. The greenery has overflowed all over the balustrade and stone steps, cracked the mosaics and climbed up statues and ornaments. Scattered around the damaged floor of the terrace, a handful of Europe’s musical geniuses relax in battered basket chairs. They are smoking cigars, perspiring and looking a trifle unshaven. Someone is laughing, so he is blurred. That’s Alfred Cortot. Jacques Thibault is leaning forward to say something and has tipped his hat down over his nose. Edwin Fischer is propping his stomach on the balustrade. Mathilde von Merkens is holding a cup of coffee in one hand and a cigarillo in the other. Vogler has closed his eyes and his waistcoat is unbuttoned. Furtwangler has seen the camera and managed to arrange a demonic smile. A few women’s faces can just be seen behind the tall windows, ageing, swollen, careworn. A young woman exquisitely dressed and coiffed is standing a little to one side, her beauty oriental. That is Andrea Vogler-Corelli. She is holding her five-year-old daughter by the hand.

The stucco is flaking off the wall, a windowpane has been replaced with a square of wood, a Cupid has lost its head. The picture radiates a good dinner, perspiring heat, lechery and gentle decay. After these gentlemen have belched, farted and had their laced coffee, they presumably gather in Mathilde von Merkens’ huge salon, with its smell of mould, and there they make music. They are, like the angels, perfect.
— (book version on archive.org (PDF), Swedish version on gBooks has the same spelling.)

Now, that is some story telling.
Details, details and details that "they" were invited to the castle, not Bergman himself, despite all of the colourful description, despite young Bergman actually being in Germany himself in the 1930s. At least it's clear that it is not a firsthand eyewitness account.

Review of that text emphasises fictional elements

A review of this book makes clear that Andrea Corelli-Vogler would be a made up name, at least, if not a made up person and the whole story at this point quite embellished:

The person to whom Bergman devotes the most space in his book (apart from himself, of course, and his father and mother) is an old pianist, to whom he gives the name Andrea Vogler-Corelli. He tells her life in a rambling way, with lust, with romantic colourfulness. To be precise, he probably tells (as in some luminous childhood episodes that can hardly be understood as literally "true") the film his imagination has made of Andrea Vogler's life, in scenes, in pictures.

The central moment (he describes it as if there were a photograph of it) shows a group of famous musicians of the thirties who met as guests at a castle near Stuttgart: "The picture radiates a good meal, sweaty heat, lust and quiet decay. After these gentlemen burp, let off the wind and have a drink in the evening, they make music. Then they are like angels - consummated."

With this picture Bergman has grasped what he knows to say about himself, about the artist, about the artists: In reality they may be pigs, but in their art, in the moment of success, they are angels.

Characters mentioned, real or not?

This becomes more clear if we try to look for the musicians mentioned: Casals, Rubinstein, Fischer, Kreisler, Furtwängler, Menuhin and Vogler. Have they ever met at all? Regularly in a big salon in a 'castle' in Stuttgart? In the 1930s? Menuhin, Kreisler 'the Jews' and Furtwängler?

And

Rubinstein was disgusted by Germany's conduct during the war and never played there again. His last performance in Germany was in 1914

Or the here all important Jonathan Vogler. Did he exist?

Well, sort of, as Max Strub he did:

The character of the famous cellist Felix in the film comedy All These Women (1964) by the Swedish director Ingmar Bergman is loosely based on the German violinist Jonathan Vogler, a pseudonym for Strub.

(Notice that in the original slott may mean 'really big house/mansion' (The Penguin English translations has it set in italics). While the review article makes it sound as 'all made up', this is for example not the case for 'Andrea Vogler-Correlli', as Andrea Corelli was a real life person and teacher to another real person in that section of book: Käbi Alma Laretei. (Her WP page)

But Max Strub wasn't as Vogler married to Andrea Corelli, but with Maria-Luisa Strub-Moresco, who was the pianist instructor for Bergman's wife Käbi:

In Bergman's films you often see the same characters reappear in different appearances and disguises. Is Maria-Luisa one of them?

In his books she appears under the name Andrea Corelli, in his films she is often the wise old woman, like the grandmother in Fanny and Alexander, who would be the perfect archetype of Maria-Luisa.
_{— Samantha Dearo De Oliveira (and Hartmut Welscher): "Die gelben Koffer. Jüri Reinvere über die Freundschaft mit Ingmar Bergman und dessen Frau, der Pianistin Käbi Laretei", 28.9.2016. English version.}

The very name Vogler then re-appears in Bergman's movies as follows:

While Elizabeth has perhaps voluntarily renounced being an actress by becoming mute, Alma is involuntarily and painfully engaged in becoming that Elizabeth Vogler, the performer, who no longer exists. Still, nothing we see justifies describing this scene as a real event - something happening in the course of the plot on the same level as the initial removal of thetwo women to the beach cottage. But neither can we be absolutly sure that this, or something like it, isn't taking place. After all, we do see it happening.[…]

Both Corliss and Young point out that Elizabeth shares the same last name, Vogler, with the magician-artist in The Magician. […]

Bergman, who wrote the film script while hospitalized in 1965, would later claim that making Persona saved his life or, more precisely, his life as an artist. For this reason, the dilemma of the actress Elisabet Vogler is typically seen as a projection of the director's own artistic crisis. […]

Although Elisabet Vogler personifies the dilemma of the modern artist, she is also a member of Sweden's cultural elite; thus her class status is quite different from that of the nurse who cares for her. The interaction between Elisabet and Alma, while certainly raising the issue of the fragile nature of personal identity can also be understood as an expression of class envy and exploitation.
_{Excerpts from — Lloyd Michaels (Ed): "Ingmar Bergman's Persona", Cambridge University Press: CAmbridge New York, 2000.}

Looking for Mathilde in all the wrong places

I don't find a prominent aristocrat, or 'industrial magnate' called 'von Merkens'. What we do see is a famous person called Peter Heinrich Merkens, in Cologne, founder of the bank *Seydlitz & Merkens'. And his family was for a time in possession of the 'Villa Merkens', now Haus im Turm. A large house built on medieval castle foundations but heavily rebuilt through the ages. Last owner through the 1930s: Ghislaine Merkens. Still not ennobled.

If the particle von is of any significance here for the character of Mathilde, then we might have some luck looking for a baron? Baron von Merkens is found in Vargtimmen, lit. 'The Wolf Hour', a fictional character from one of Bergman's movies:

The only inhabitants on the island are the Von Merkens, an anachronistic aristocratic family, who can be seen as amalgamations of characters from the opera serving to mete out the failed hero’s punishment. Like the Queen of the Night, who feels impoverished as she only bears the power of Night, the Von Merkens suffer twentieth-century fiscal angst as they literally bankrupt due to fiscal mismanagement by one of their members. In their mansion, reason is overwhelmed by illusions fueled by twentieth-century anxiety, often achieved cinematically: a nightmarish look via over-exposure, unusual angles, faces that peel off, a character who “climbs the wall,” etc. While the film has no musical score, the sound scape is anything but trivial as it contributes to the unreal “look and feel” of the film. One of the primary techniques is analectic sound, “the selection and amplification of only one or two identifiable sounds from out of the natural ambience [which] create[s] a mood of eerie hopelessness.” Bergman, not unlike a composer, selects what we will – and will not – hear. The departure from the soundscape of the “natural world” is left behind as Johan and Alma arrive on the island. Most unlike the composer Mozart who provided a logically arranged score which underpins the journey toward Enlightenment for the major characters, Bergman’s “score” distorts the soundscape in the illogical world that serves as Johan’s punishment.

The Von Merken matriarch, combining the Queen of the Night and Papagena, is introduced as she mysteriously appears on the scene to address Alma. As in the opera, magic and mystery dominate the character as she projects the feeling of coldness from her hand to that of Alma’s. With the Queen of the Night, Bergman foreshadows his treatment of the opera in depicting her face. Our first glimpses of the matriarch seem “natural” enough, just as does that of the Queen in Bergman’s cinematic setting of the opera. When the characters’ “true sides” are subsequently observed, however, the Queen, almost bald, is soaked in an achingly cold blue light during her revenge aria. In Vargtimmen, the matriarch’s “true face” is actually no face at all. When she removes her hat, we observe a skull with eyes relocated to a drinking glass.
_{— Ellen J. Burns: "Ingmar Bergman’s Projected Self: From W. A. Mozart’s Die Zauberflöte to Vargtimmen", in: Anna-Teresa Tymieniecka (Ed): "Phenomenology of Life from the Animal Soul to the Human Mind. Book II The Human Soul in the Creative Transformation of the Mind" pp 459–468, Analecta Husserliana The Yearbook of Phenomenological Research Volume XCIV, Springer: Dordrecht, 2007.}

Two other instances of the perverse way in which jealousy increases sexual passion in Hour of the Wolf verify the mechanism in Johan. The Baroness Von Merkens, Corinne, desires her lovers to leave marks on her from sexual intercourse in order to arouse her husband, and the Baron, while literally "climbing the walls" in anger over Johan's rendezvous with Veronica Vogler, who is now his mistress, only promises to watch the coupling as a voyeur.[…]

Earlier, at the dinner table, Baron Von Merkens, who claims to be a patron of the arts, has told everyone about a little joke he pulled on another artist.
_{— "The Case of Ingmar Bergman"}

Looking through the usual registers, wikis, phone books: nowhere in Germany any family 'von Merkens' appears. It appears to be at least a pseudonym.

Begrman's 'method writing'

From a review:

Laterna Magica shows how difficult it is to define that odd word, "autobiography". Bergman isn't very interested in telling you what happened, though you absolutely don't get the feeling that he's trying to hide anything from you either.[…]
So don't read this book if you hope to find out the truth …

And finally:

The Magic Lantern is of interest from an intermedial perspective in its forthright theatricalization or cinematization of the written text and the self-conscious performativity of its authorial voice. Of particular interest is the way the narrator turns into a kind of distanciated autobiographical witness, which in turn reminds the reader of the inherent narrative split in the autobiographical genre between the enunciating subject speaking from the present, and the described subject, the younger self in the past. In doing so the narrator seems to turn language itself into a performative venue: the medium of words becomes a theatrical stage or a cinematically charged mise-en-sce`ne for memory as such. This is of course not only stylistically elegant, for what can be more natural than a film- and theater director who, as the very title of the autobiography announces, turns memories into cinematic and theatrical performances? But even more interesting is the extent to which Bergman in doing so seems to conjur forth his biographical legend, reminding the reader of who is in charge of text: the narrator becomes the director of the text, so to speak, lighting and setting the stage.

Besides this artful approach, Bergman also clearly fictionalized his life in other ways, which is corroborated by the private note books and original manuscripts that the writer of this paper has gained access to.
_{— Maaret Koskinen: "Ingmar Bergman, the biographical legend and the intermedialities of memory", Journal of Aesthetics & Culture, 2:1, 5862, (2010), DOI: 10.3402/jac.v2i0.5862}

Or in his own words:

Self-portraiture is something one should never get involved in, since it is wrong to lie even though one endeavours to tell the truth.
_{— "Ingmar's self portrait" (1957) as quoted in "Who is he really?"}

I'm planning, you see, to try to confine myself to the truth. That's hard for an old, inveterate fantasy martyr and [illegible] liar who has never hesitated to give truth the form he felt the occasion demanded.
_{– On his plans for his autobiography Laterna Magica, as quoted in "Who is he really?"}

Clues from real persons mentioned

Since Käbi Laretei is the alleged source for these happenings, and her being a real person with real name, there is one interesting letter addressed to her, while she was in Germany, as Bergman's wife in 1961: Richard-Wagner-Str 12. A "Pension Reizenstein" at the time, now a commercial building, housing a few modern companies. The thing is: it is quite big and has a small tower attached at the north-west edge:

Too late to be definitive anything for "1930s", but if she liked the surroundings and 'came back', one address to look into for what happened there in terms of musical events. Käbi's own book "Toner och passioner: Ludus Tonalis" seems to mention Stuttgart and Marialuisa a few times, but my access to it is too limited. But it's noteworthy that she writes:

Ingmar used to say that he learned more about film from Marialuisa than from anyone else. He often sat next to us during our lessons and he described her in his autobiography, albeit under a pseudonym.

While Maria-Luisa and Bergman were introduced to each other in Stuttgart, Käbi writes that Max and Maria-Luisa were at one time staying in Mecklenburg at some baroness Fides von der Malsburg, more precisely Fides Eleonore Davida Richardis Ida von der Malsburg (Rabe von Pappenheim), born 1884, member of an old-nobility family from Hesse.

In a long chapter in The Magic Lantern, Bergman probes the history of Strub-Moresco’s (In his writings, Bergman assigns to Strub-Moresco the particularly Bergmanesque pseudonym Andrea Vogler-Corelli. She was married to the German violinist Max Strub; while his career is documented through concerts and recordings, hers is not.) education and subsequent struggle in captivity during World War II, revealing one of her “mad, bizarre, obscene and comical” stories as his source for the story behind his farcical flop, All These Women (För att inte tala om alla dessa kvinnor, 1964). He then recounts one of the many lessons he witnessed between Strub-Moresco and Laretei; “rigorous standards” were applied to each phrase, “plucked apart into its constituent parts, practised with pedantic fingering for hours, then reassembled when the time was right”. To a musician (and I speak as one myself), this style of teaching between two professional adults seems preposterous, almost cruel and certainly unmusical. Yet Bergman found Strub- Moresco’s methods admirable, even inspirational, comparing what he considered the sloppiness and ignorance of theatre to her precise technical instructions. In musical descriptions that appear both in his autobiographical text and in his screenplays, he imitates the language that he ascribes to her – quotation marks in his text indicate her speech rendered apparently verbatim, twenty years after listening:

No padding in Beethoven, he speaks persuasively, furiously, sorrowfully, cheerfully, painfully, never mumbling. You mustn’t mumble, never produce common stuff! You must know what you want even if it’s wrong. Meaning and context … That doesn’t mean everything has to be emphasized; there’s a difference between emphasis and significance.

This passage, uttered by Strub-Moresco during a lesson, sounds suspiciously like Charlotte from Autumn Sonata, a concert pianist giving a lesson to her daughter (a film for which Laretei recorded both versions of the Chopin prelude played onscreen and coached the actresses for their performance scene):

Chopin isn’t sentimental, Eva. He’s very emotional but not mawkish. There’s a huge gulf between feeling and sentimentality. The prelude you played tells of suppressed pain, not of reveries. You must be calm, clear, and harsh … Total restraint the whole time. Chopin was proud, sarcastic, passionate, tormented, furious, and very manly … This second prelude must be made to sound almost ugly. It must never become ingratiating. It should sound wrong. You must battle your way through it and emerge triumphant.

The similarity of these quotes reminds us of Meryman’s observation that Bergman’s characters constantly articulate his recollections and philosophy. But here the Bergman– Strub-Moresco–Laretei triptych complicates matters. It could be that Charlotte was based on Strub-Moresco. It could also be that Strub-Moresco was based on Charlotte, or that the borders between them blurred, illusion and reality becoming the same thing in Bergman’s memory. Whatever the case, Bergman’s education by proxy gave him access to a prestigious musical lineage that included Edwin Fischer, Pablo Casals, Artur Rubinstein, Fritz Kreisler, Wilhelm Furtwängler, Alfred Cortot, Jacques Thibault, and Yehudi Menuhin, musicians with whom Strub-Moresco claimed to have either studied, spent time, or collaborated. Bergman also attributes part of his understanding of The Magic Flute to her. On the night Laretei gave birth to their son Daniel, so the story goes, Strub-Moresco opened the opera score and engaged Bergman in a discussion of how Mozart, a Catholic, chose a Bach-inspired chorus (Lutheran) for his message. She then flipped to “Bei Männer, welche Liebe fühlen”, the duet between Papageno and Pamina, and said, “Here’s another message. Love as the best thing in life. Love as the innermost meaning in life.” Bergman would repeat this sentiment of life and love in his films, in his texts, and when offering his own interpretations of Mozart in film and words. He would also frequently reference discussions he apparently had with Laretei that uncovered hidden meanings in Beethoven, Handel, Chopin, Bach, Schumann, and others. He compared their compositions to architecture, attributed musical phrases to bits of dialogue, and referred to their writings and letters as a way towards musical interpretation. Using these little stories, he wove a complex web of circular cause and consequence. Who is speaking, his fictional characters, fictionalised versions of real people, the real people themselves, or he himself? Who is qualified to speak?
_{— Anyssa Charlotte Neumann: "Sound, Act, Presence. Pre-Existing Music in the Films of Ingmar Bergman", Dissertation, King's College, London, 2016. (PDF)}