Looking for a quote, sutta or teaching about suffering not decreasing with succedent stages of enlightenment

I don't know about a quote or a video, but to me this is straightforward from the three marks of existence. When you say 'stages of enlightenment' I assume you mean all those times before enlightenment which of course are bound up with samsara and hence have the three marks of existence.

The first mark of existence is anitya or impermanence. The relevant point here is that this mark of impermanence characterizes each and every moment. There is no moment of existence not characterized by this mark of change. This is true of all of those existing moments along those stages of enlightenment.

The second mark of existence is dukkha or suffering. Now, "suffering" is technically not a great translation, but this is what I believe you are referring to in your question: dukkha. There are three kinds of dukkha:

1. The suffering of pain - which happens to everyone including Bodhisattvas
2. The suffering of change - which is pleasure to pain or pain to pleasure or the change associated with the first mark
3. All pervasive suffering - existential pain or just the pervasive feeling of nothing being quite right

Just from a cursory look at these definitions it is clear that all three correspond to sentient beings. The last two are with us constantly while the first one comes and goes. Moreover, it is hard to understand how these - being literal marks of existence - not pertain to any sentient existing being regardless where they are on the path. If you are on the path and haven't reached the goal you are subject to these marks of existence.

And indeed I think it could very well be the case that further progress on the path can lead to more not less of say #1 at least. Bodhisattvas are regularly depicted as voluntarily going into the depths of hell to save sentient beings and thus subjecting themselves to the worst kinds of pain. The latter two are with us more or less constantly although when our minds are focused on virtue they do seem to abate or at least do not overpower us so much. At least that is my experience.

The Visuddhimagga or the Path of Purification by Ven. Buddhaghosa talks about this. Please see "Path of Purification (Visuddhimagga)", translated from Pali by Ven. Ñāṇamoli. It's a classic manual of Buddhist doctrine and meditation written in approximately the 5th century CE, and is considered the most important Theravada text outside the Pali Canon and its traditional commentaries.

It talks about the eight knowledges of insight:

Now, insight reaches its culmination with the eight knowledges, and knowledge in conformity with truth is ninth; these are what is called purification by knowledge and vision of the way.The eight should be understood as follows: (1) knowledge of contemplation of rise and fall, which is insight free from imperfections and steady on its course,(2) knowledge of contemplation of dissolution, (3) knowledge of appearance as terror, (4) knowledge of contemplation of danger, (5) knowledge of contemplation of dispassion, (6) knowledge of desire for deliverance, (7) knowledge of contemplation of reflection, and (8) knowledge of equanimity about formations.

“Knowledge in conformity with truth as ninth” is a term for conformity.So one who wants to perfect this should make these kinds of knowledge his task, starting with knowledge of rise and fall free from imperfections.

The description of (3) knowledge of appearance as terror:

As he repeats, develops and cultivates in this way the contemplation of dissolution, the object of which is cessation consisting in the destruction, fall and breakup of all formations, then formations classed according to all kinds of becoming, generation, destiny, station, or abode of beings, appear to him in the form of a great terror, as lions, tigers, leopards, bears, hyenas, spirits, ogres, fierce bulls, savage dogs, rut-maddened wild elephants, hideous venomous serpents,thunderbolts, charnel grounds, battlefields, flaming coal pits, etc., appear to a timid man who wants to live in peace. When he sees how past formations have ceased, present ones are ceasing, and those to be generated in the future will cease in just the same way, then what is called knowledge of appearance as terror arises in him at that stage. ...

But does the knowledge of appearance as terror [itself] fear or does it not fear? It does not fear. For it is simply the mere judgment that past formations have ceased, present ones are ceasing, and future ones will cease. Just as a man with eyes looking at three charcoal pits at a city gate is not himself afraid, since he only forms the mere judgment that all who fall into them will suffer no little pain;—or just as when a man with eyes looks at three spikes set in a row, an acacia spike, an iron spike, and a gold spike, he is not himself afraid, since he only forms the mere judgment that all who fall on these spikes will suffer no little pain;—so too the knowledge of appearance as terror does not itself fear; it only forms the mere judgment that in the three kinds of becoming, which resemble the three charcoal pits and the three spikes, past formations have ceased, present ones are ceasing, and future ones will cease.

The description of (4) knowledge of contemplation of danger:

As he repeats, develops and cultivates the knowledge of appearance as terror he finds no asylum, no shelter, no place to go to, no refuge in any kind of becoming, generation, destiny, station, or abode. In all the kinds of becoming,generation, destiny, station, and abode there is not a single formation that he can place his hopes in or hold on to. The three kinds of becoming appear like charcoal pits full of glowing coals, the four primary elements like hideous venomous snakes (S IV 174), the five aggregates like murderers with raised weapons (S IV174), the six internal bases like an empty village, the six external bases like village-raiding robbers (S IV 174–75), the seven stations of consciousness and the nine abodes of beings as though burning, blazing and glowing with the eleven fires (see S IV 19), and all formations appear as a huge mass of dangers destitute of satisfaction or substance, like a tumour, a disease, a dart, a calamity,an affliction (see M I 436). How?

They appear as a forest thicket of seemingly pleasant aspect but infested with wild beasts, a cave full of tigers, water haunted by monsters and ogres, an enemy with raised sword, poisoned food, a road beset by robbers, a burning coal, a battlefield between contending armies appear to a timid man who wants to live in peace. And just as that man is frightened and horrified and his hair stands up when he comes upon a thicket infested by wild beasts, etc., and he sees it as nothing but danger, so too when all formations have appeared as a terror by contemplation of dissolution, this meditator sees them as utterly destitute of any core or any satisfaction and as nothing but danger.

Apparently, this will transition into a knowledge of peace:

“He contemplates as suffering
Arising, occurrence, and the sign,
Accumulation, rebirth-linking —
And this his knowledge is of danger.

“He contemplates as bliss no arising,
And no occurrence, and no sign,
No accumulation, no rebirth-linking —
And this his knowledge is of peace.

“This knowledge about danger has
Five sources for its origin;
Knowledge of peace has also five —
Ten knowledges he understands.

Knowledge of the state of peace is this: “Non-arising is safety,” etc.: this, however, should be understood as said for the purpose of showing the opposite kind of knowledge to knowledge of danger. Or when it is stated in this way, that there is safety without terror and free from danger, it is for the purpose of comforting those who are upset in their hearts by seeing danger through appearance as terror. Or else, when arising, etc., have clearly appeared to a man as terror, his mind inclines towards their opposites, and so this is said for the purpose of showing the advantages in the knowledge of danger established by the appearance as terror.

So, the mind first sees the terror of the inevitability of the cessation of phenomena, and then experiences danger when it realizes that there is no place to cling to for safety from the inevitability of the cessation of phenomena. Finally, it accepts this situation, and sees non-arising etc. as safety.

Hence, to me, the knowledge of appearance as terror and knowledge of contemplation of danger sound like the increasing of suffering as one progresses on the path to liberation.

For those on the Noble Eightfold Path, disagreeable things in general decrease over time:

MN46:4.3: So they cultivate and foster practices they should, and don’t cultivate and foster practices they shouldn’t.
MN46:4.4: When they do so, unlikable, undesirable, and disagreeable things decrease, and likable, desirable, and agreeable things increase.

But there are four ways to practice. In particular, let's look at the painful ones. First the practice to avoid current and future pain decreases pain by avoidance, so it doesn't lead to an increase in suffering:

MN46:5.3: There is a way of taking up practices that is painful now and results in future pain.

Second, if we avoid pleasant things to avoid future pain, then a hedonist might consider that a "momentary increase of suffering". An example might be avoiding exciting and loud music concerts to prevent future deafness:

MN46:5.4: There is a way of taking up practices that is pleasant now but results in future pain.

Third, we do or endure something painful now for future pleasure:

MN46:16.2: It’s when someone in pain and sadness doesn’t kill living creatures, steal, or commit sexual misconduct. They don’t use speech that’s false, divisive, harsh, or nonsensical. And they’re contented, kind-hearted, with right view. Because of these things they experience pain and sadness.
MN46:16.12: But when their body breaks up, after death, they’re reborn in a good place, a heavenly realm.
MN46:16.13: This is called the way of taking up practices that is painful now but results in future pleasure.

This third practice it tough. It has us face and deal with painful things instead of running away from them or giving in to anger. Some may choose to see this as an "increase in suffering", but even that increase is momentary, since in the long run suffering lessens overall.

As practice deepens, our awareness increases about what results in future pain. And with an increased awareness of future pain, we act now to avoid that future pain. Paradoxically, that ever-sharpening awareness of future pain leads to contentment with fewer and fewer wishes.

The whole point of being a Sotapanna and higher stages is to know the dharma, and that there is an end to suffering and know that things will go well for them. It's impossible to have suffering increasing, especially by simple perceptions. It is actually the non-enlightened people who freak out when they hear the dharma https://suttacentral.net/an4.33/en/bodhi

The only framework where terror arises is the made up 16 knowledges which are not found in the sutras. like ruben explained https://buddhism.stackexchange.com/a/47543/14789

The fears sotapanna and so on have is to make moral mistake, ie breaking the precepts and so on.

Then Anathapindika the householder went to the Blessed One and, on arrival, having bowed down to the Blessed One, sat to one side. As he was sitting there, the Blessed One said to him, "When, for a disciple of the noble ones, five forms of fear & animosity are stilled; when he is endowed with the four factors of stream entry; and when, through discernment, he has rightly seen & rightly ferreted out the noble method, then if he wants he may state about himself: 'Hell is ended; animal wombs are ended; the state of the hungry ghosts is ended; states of deprivation, destitution, the bad bourns are ended! I am a stream-winner, steadfast, never again destined for states of woe, headed for self-awakening!'

"Now, which five forms of danger & animosity are stilled?

"When a person takes life, then with the taking of life as a requisite condition, he produces fear & animosity in the here & now, produces fear & animosity in future lives, experiences mental concomitants of pain & despair; but when he refrains from taking life, he neither produces fear & animosity in the here & now nor does he produce fear & animosity in future lives, nor does he experience mental concomitants of pain & despair: for one who refrains from taking life, that fear & animosity is thus stilled.

"When a person steals... engages in illicit sex... tells lies...

"When a person drinks distilled & fermented drinks that cause heedlessness, then with the drinking of distilled & fermented drinks that cause heedlessness as a requisite condition, he produces fear & animosity in the here & now, produces fear & animosity in future lives, experiences mental concomitants of pain & despair; but when he refrains from drinking distilled & fermented drinks that cause heedlessness, he neither produces fear & animosity in the here & now nor does he produce fear & animosity in future lives, nor does he experience mental concomitants of pain & despair: for one who refrains from drinking distilled & fermented drinks that cause heedlessness, that fear & animosity is thus stilled.

"These are the five forms of fear & animosity that are stilled."

— AN 10.92