Google App Engine doesn't have many users, and isn't a focus for future engineering effort.
Either people need to start using it for serious projects (rather than just demo guestbook projects), or it'll be shut down in a future round of closures.
That's a big question :). I don't think they're mutually exclusive. GKE provides more flexibility but requires more configuration. GAE is less flexible but more "serverless". GKE is probably more expensive for a single app, so I'd probably pick GAE for a single app. For a _project_, I'd have to understand more about what I'm building and what I need.
I'd also probably use Cloud Run over GAE, but that's a personal preference because I've been working closely with that product lately.
Google App Engine seems to be a very fragile service. From Sept. 2019 It's going down every month. 10 hour+ outage in July, Sept. and Oct.
For the premium they charge for App Engine, one would expect the service to be more reliable.