> I guess the term “Serverless” is pretty ambiguous, (...)

I don't this is the case though.

The core principle of serverless computing is that a cloud provider supplies a managed service and scales computational resources allocated to the service to meet it's computational needs.

This "serverless postgres" meets none of the items in the definition.

You mentioned AWS Lambdas. AWS allocates all computational resources when a function is invoked.

Let's face it: this was an attempt to abuse a buzzword.