These are my thoughts. They may be mistaken.
I agree with Anālayo that they are problematic to some extent. I think that it is perfectly reasonable that the historical Buddha taught that there were past Buddhas who had, or could have, realized this Dhamma before and taught it. I think as far as the suttas are concerned, this is a basic point of Buddhology: Buddhas are a kind of cosmic role, much like Buddhist deities, who re-appear cyclically. Sakka—the traditional lord of the gods—is not an immortal deity but rather a position in a cosmic order into which one can be reborn.
I think we can see several ways in which this cyclic, cosmic Buddha narrative is mythologically significant. I have just named one, that is, the Buddha is elevated to the position of a cosmically significant position akin to a deity. This is the exact same trajectory that developments in later Buddhology took: they gradually deified the Buddha and pushed his existence further back in time with the Jātakas and the idea of the perfections. They even pushed his existence forward in time first with a coming Metteyya Buddha and then with the idea of Buddhas who are in Pure Lands, stay in Saṁsāra, manifest in different bodies some of which are more permanent, Buddha-nature as a cosmic entity, etc.
The other way in which it seems mythologically significant is its relationship to Brahmanism. In the suttas, the earliest form of ‘past Buddhas’ are the 7 past Buddhas. That is to say, there is our Buddha, and there are a number of Buddhas going back seven “generations”. This is a parallel of Brahmanical value: The brahmins in the suttas consistently talk about how a lineage is authenticated by going back 7 generations with fathers, teachers, mothers, hermits, sages, seers, poets, etc. It begins with the 7 ṛṣis, and even this goes back further to other non-Indic cultures—probably having to do with the constellations and the Big Dipper which has 7 stars.
This means that the 7 Buddhas happen to authenticate the lineage of the Dhamma back 7 generations with previous, mythological, historical sages in the exact way that the Brahmins and the Jains did. The Jains also taught that they had a lineage of past awakened beings. The Buddhists were missing this: It was just the Buddha and his followers. No ancient texts; no lineage of ancient sages. Well, unless they introduce it.
Is it authentic? I don’t know. Like I said, these past Buddhas are found in all kinds of suttas. They sometimes correspond to clearly later ideas like the wheel-turning monarch destiny which may be an indication of their relative lateness. They appear in formulaic passages (like at the beginning of the SN where they are just stock-suttas with repeated formulas and no new doctrinal information), and in literary narratives which are clearly more mythological and building on earlier ideas, like the story of Vipassī Buddha at DN 14.
I think the principle of Buddhas being able to arise in the past and future and re-discover the Dhamma holds true. The authenticity of specific past Buddhas with these names that the Buddha himself encountered though? We cannot be sure, but I think they can be valued more for their mythological and cosmological significance rather than their specific authenticity. Note that this is not a dismissal of the ideas; mythology does not mean useless untrue stories. It just means, among other things, stories which are less about historical fact and more about meaningful presence in the minds of the current people telling them.