I hadn't heard of throwing money at it before.

Maybe "Two Generals" doesn't work, but "Two Rich Generals" does.

If you compare prices vs cloud managed Postgres it's not that expensive.

Or rather, cloud managed Postgres is expensive, especially once you get into the cloud-specific forks of it that try to make it scale, because AWS/Azure/etc know that people will pay a lot of money for the Postgres brand but don't want to admin it themselves.

So the moment you commit to paying for a managed database you should check out the prices to rent an Oracle DB and see how it compares, especially because they flex well so on the smaller end it can end up being cheaper as you're renting only part of a machine. Plus a lot of times people will tell you that Postgres can do this or that, but then it requires some custom extension that is not necessarily available in your cloud's managed product. A lot of stuff that's extensions in Postgres are out of the box features in Oracle e.g. message queues or JavaScript support.

How much does it cost to rent a db that can do CAP?

What do you mean by do CAP?

If you mean the CAP theorem then that's an impossibility result, so...