"My" instance of sqlite that they host?
yeah, that is my understanding, if I understand your question correctly.
Of course it is all hidden from view, there is a merkle tree involved, and you probably want to use a higher level client than SQL
This talks about why SQLite and not Postgres
https://github.com/bluesky-social/atproto/discussions/2287
Repository spec:
https://atproto.com/specs/repository
Small program to export:
https://github.com/bluesky-social/cookbook/tree/main/go-repo...
I believe each user gets a dedicated sqlite database, or at least a dedicated repo. I recall reading somewhere about the implementation moving to use sqlite