Does there exist a historical-critical study ("Higher Criticism") of Buddhists’ texts?

The jātakas and avadānas are obviously untrue because the word 'jati' & 'nivasa' found in the suttas do not mean 'physical birth' or 'past lives'. 'Jati' is defined in SN 12.2 as the birth of a class of beings and the word 'beings' is defined in SN 23.2 & SN 5.10 as a 'view'. Therefore, 'jati' refers to 'mental/conceptual birth' rather than 'physical birth'; as clearly expressed in MN 86, where the Buddha said to Aṅgulimāla his becoming a monk was 'birth into the noble birth' . Similarly, the word 'nivasa' means 'home', 'abode' or 'dwelling' and SN 22.79 makes it literally clear that recollection of 'past abodes' (generally mistranslated as 'past lives') is recollecting in the past when the mind ignorantly regarded one or more of the five aggregates to be 'self'.

Its important to recognise, due to its own internal perversions & external social mischief, Buddhism became extinct in India. Since the Jains continued to exist after the Muslim conquests, obviously the Hindu (political vassals) & Muslim (rulers) decided to end Buddhism because Buddhism kept appropriating Hindu doctrines & deities for mischievous worldly purposes. The Buddhist laypeople of Western & Eastern India were converted to Islam; but Hinduism & Jainism remained.

The evolution of the Buddhist texts & sects is clear. The jātakas and avadānas (such as the Buddhavaṁsa, Therāpadāna & Therīapadāna) redefined the meaning of "jati" and resulted in the addition of perverted suttas into the Sutta Pitaka; such as Iti 22, SN 22.96, AN 3.15, AN 9.20, MN 81, MN 83, MN 50, DN 19 & MN 123. Most of these suttas about literal past lives contain the term “ahaṃ tena samayena”, which is found at least 22 times in the Buddhavaṃsa, twice in the Therāpadāna and once is the Therīapadāna.

The supernatural MN 123 shares the term mātukucchismiṁ with other obvious late texts such as DN 15, DN 28 & DN 33. This notion of mātukucchismiṁ & the Theravada idol DN 15 appear not found/discussed in later early commentaries, such as the Paṭisambhidāmagga or Abhidhamma Vibangha; which support the view these are late & non-essential suttas.

I could recommend my own critical studies of Buddhist texts called Is “rebirth” a misconception of the Pali suttas? and Dependent Origination from the Pali Suttas but this used to be against the rules of this forum therefore I will not recommend these critical studies.

For very superficial theories ('studies'), you can try the authors named Brahmali, Sujato & Analayo, such as: The Authenticity of the Early Buddhist Texts

There are studies but they are conjecture for the most part. The conclutions derived are based on historicist philology that can hardly be applied with confidence. No one will accept this method (for example) in a Criminal Investigation.

• Which groups and which interests triggered the texts and their dissemination?

The Buddha mentioned "Jataka" as part of the Navanga-satthu-sasana (ninefold dispensation of the teacher) in Suttas.

I assume that most of these stories are fiction. Therefore my question: • Do these texts or figural representations raise any truth claim?

The Theravadins have slightly different stories. Many of Jatakas and Apadanas have been sensibly dated back to the Buddhas time by many scholars.

• If yes: Which claim? How can one validate the truth claim?

Robert E. Buswell (2004). Encyclopedia of Buddhism: "Jātaka tales may be quite ancient. The term appears as part of a schema of Buddhist literary forms called the nine component genres of the Buddha's teaching (navaṅga-buddhasāsana), and depictions of them appear in early Indian art (as early as the second century BCE)."

Straube, Martin. Narratives: South Asia in Silk,"Brill's Encyclopedia of Buddhism": "While these texts cannot be dated in a precise manner, "the fact that many narratives are passed on in almost identical form within the canons of the different schools shows that they date back to the time before the schisms between the schools took place."

There are scholarly evidences, but the main evidence is derived by studying Tipitaka. If one realized that the fundamentals described in Tipitaka are true, then he will reasonably trust the stories comes in Tipitaka for the most part.