Supabase covers the parts of Firebase most projects actually use: a database with an API in front of it, authentication, storage and realtime updates. The difference underneath is that the database is Postgres, which changes what you can do later.
What you are replacing
Firebase is attractive because a client can talk to it on day one with no backend written. What it costs is a data model that is hard to query in the ways you eventually want, and a bill that follows read volume rather than data size.
The feature list maps closely enough that a small app can be moved without redesigning it, and the storage layer being Postgres means joins, constraints and SQL reporting are available from the start rather than after a migration. Row level security is where authorisation lives, so the rules sit next to the data.
What it does not replace
It is more infrastructure than Firebase, whether you host it or not, and the mobile SDK ecosystem is younger. Row level security is also a real skill: written carelessly it is a hole rather than a boundary.
Stay on Firebase when the product is a mobile app with simple access rules and the team has no interest in databases. The moment reporting queries or per tenant rules appear, that calculation changes.