Note that this already exists on top of SQLite proper - authored by Ben Johnson (Litestream, Fly.io etc.) - https://github.com/benbjohnson/postlite
Something like https://github.com/benbjohnson/postlite ?
I've not use this myself, but Ben Johnson's https://github.com/benbjohnson/postlite in front of SQlite might allow you to use PostgREST? I recall him saying on a podcast that his goal was to be able to point the large ecosystem of PG tools at SQlite.