Can’t speak for anyone but myself and my experience anecdotally, having used Databricks: I consider them to be the Oracle of the modern era. Under no circumstances would I let them get their hooks into any company I have the power from preventing it.
Why do think so? Databricks notebook product I have used in couple of companies is pretty solid. I have done any google research but they are generally known to be very high talent dense kind of place to work.
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_.
Either way, there are plenty of other serverless Postgres options out there, Supabase being one of the most popular.