Serverless in the context of Postgres means to decouple storage and compute, so you could scale compute "infinitely" without setting up replica servers. This is what Neon offers, where you can just keep hitting their endpoints with your pg client and it should just take whatever load (in principle) and bill you per request.

Supabase gives you a server that runs classic Postgres in a process. Scaling in this scenario means you increase your server's capacity, with a potential downtime while the upgrade is happening.

You are confusing _managed_ Postgres for _serverless_.

Others in the serverless Postgres space:

- https://www.orioledb.com/ (pg extension)

- https://www.thenile.dev/ (pg "distribution")

- https://www.yugabyte.com/ (not emphasizing serverless but their architecture would allow for it)