We do also use their auth, storage, api, etc. But even if you just want to host a postgres db it's still worth checking out I think.
It's managed postgres, 2 free db's, connection pooler, super easy read replicas (requires a larger paid instance), backups, lots of tooling/dashboards/advisories, cli for running locally during development, database branching, backups, fdw, and lots more. All of it open source.
You can turn off the data api's etc if you just want to connect directly: https://supabase.com/docs/guides/database/hardening-data-api...