For most use-cases, Serverless Postgres is a nasty thing in my experience. It is way too slow and has a lot of latency over the wire, even for production apps.

The scaling requirement doesn't usually happen to startups until they hit ~4 years or later, and it is not much useful to optimize for it anytime before that. Add the cost aspect to it and it becomes close to meaningless.

You're way better off running your own managed Postgres service or container that costs about $10 a month.