I think this is the right analogy, contrary to some other very poor ones in this thread. Yes, it is rare to really look at commit messages, but it can be invaluable in some cases.
With vibe-coding, you risk having no documentation at all for the reasoning (AI comments and tests can be degenerate / useless), but the prompts, at bare minimum, reveal something about the reasoning / motivation.
Whether this needs to be in git or not is a side issue, but there is benefit to having this available.
Depending on the size it might make sense as a kind of commit metadata reference to external, like the signed-off-by field.
Chat-Session-Ref: claude://gjhgdvbnjuteshjoiyew
Perhaps that could also link out to other kinds of meeting transcripts or something too.