My impression of app engine is that you have to use all the cloud* services like SQL, cache, etc, which will make it significantly more expensive, even if it does that app layer fine. Is that wrong?
It's wrong today. It was true in 2008, when GAE was Google's entire cloud offering (and there was no Docker or K8s).
Around the time "Google Cloud Platform" became a thing, Google changed GAE from an encapsulated bubble into a basic frontend management system that interacts with normal services through public APIs (either inside or outside GCP). It's more expensive than GCE, but it's fully managed and lets you skip the devops team.
