Is there a standard authority on the textual history of the authors of antiquity?

While there is no single resource for the textual history of how every classical work has come down to us, there are several books and databases which contain the known raw facts as to which manuscripts exist and where they are. The relationships between these copies is almost always a matter of modern reconstruction, debated by scholars and therefore not always suitable for a fixed-form database summary. For certain authors, works, topics and periods, there may be specific resources that present a more comprehensive account; results will vary depending on how motivated scholars have been over the last several centuries to investigate a given topic. Aristotle is among the authors who are very intensely studied.

In the case of the History of Animals, the Loeb edition you cite does include an account of the manuscript sources on which its version of the text was based. These are the same as in the edition by Leonhard Dittmeyer, Aristotelis de Animalibus Historia (Teubner, 1907). They are cross-cited to Inventaire des manuscrits grecs d'Aristote by André Wartelle (1963), a catalogue of 2283 Aristotelian manuscripts. The book also covers important printed versions, whether based on these manuscripts or on other sources now lost to us. For example, one of the most important sources is given in Loeb as:

C^a Laurentianus LXXXVII. 4. 14th century. Written by Joanicius. Contains Books I–IX in the following order (which is the order normally found in the mss.): I–VI, VIII, IX, VII. Collated by Bandini against Du Val's 1619 edition for Camus; this was apparently the first time it had been used for establishing the text. Collated also by Bekker and Dittmeyer.

(References like "Camus" are explained elsewhere - for example, that means Armand-Gaston Camus who published his version of the History in Paris in 1783. So this gives some more hints about which texts were used by which authors of post-mediaeval editions as well.)

The citation "Laurentianus LXXXVII. 4" is not completely obvious; it refers to a book in the collection of the Biblioteca Medicea Laurenziana in Florence, which includes several different works by Aristotle. Its version of the History of Animals starts on the verso of f70. Much more information on this particular codex is available at its comprehensive bibliography entry of Commentaria in Aristotelem Graeca et Byzantina, which as its name suggests includes a manuscript database of the Greek and Byzantine side of Aristotle's transmission. Many more versions of the text are in its summary page.

Information there shows not only the physical structure of the manuscript and which bits of the text it contains, but also its provenance, and citations of scholars who have written about it.

Just looking through these pages, we can make some meta-observations:

1. Sources for the raw data are pretty accessible, in the sense that a great deal of information is out there on the Internet, either in modern databases, or digitizations of earlier works (such as 19th-century critical editions).
2. The data are pretty inaccessible, in the sense that fully appreciating any particular database entry might demand a knowledge of Greek, Italian and German, even aside from interpreting what is meant by "167 (κ[β´])".
3. We often do not have all that many different copies of a text, and new discoveries are rare. There may not be very much we can reasonably say about different versions and how they came about.
4. Still, a lot of authors have written a lot of words about their different theories of what is going on. There is not necessarily a single accepted version of a text's lineage.
5. Due to historical divisions within scholarship, sources will tend to focus on just one segment of the transmission. For example, it's common to find accounts which end their story at the advent of print, while different authors take up the tale of how various print editions relate to one another. There are databases for papyrus fragments, which are distinct resources from the databases for mediaeval manuscripts.

Moreover, even the apparently comprehensive information above actually omits an important part of the transmission, namely the Arabic tradition. We know that Camus' print edition, mentioned above, took account of the Latin translation by Michael Scot from about 1215, which was made from Arabic sources. It was this Latin version which tended to be used by mediaeval scholars such as Albert the Great, so that is an important part of the history of the work's reception. Additionally, the Latin has been used to inform modern versions of the Greek text. Despite all this, the first printed edition of Scot was made as recently as 2020 (by Aafke M.I. van Oppenraay). Her introduction mentions many more manuscript sources from the Arabic-Latin side, not found in CAGB. This type of prose account is probably the best way to get an understanding of what we know, and what we can infer.