It's Postgres, but bundled with some extensions and Postgrest. And a database UI. But hosted and it runs locally also by pulling the separate parts. Running it locally has issues though, so much so that I found it easier to run a docker compose of the separate parts from scratch and at that point just carry that through to a deployment, at which point is there still a reason to use Supabase rather than another hosted Postgres with the extensions?
It's a bit of a confusing product story.