You should probably stick with App Engine Standard, if you need customization of some sort and your app needs to do more than just Pub/Sub. If all you're doing is short processing of messages (e.g. pub/sub + writing to a data store), use Cloud Run.

Google Cloud offers the continuum from fully managed to fully manual infrastructure, so it really depends on how much control you want to hand over versus getting things done for you. I've engaged with teams that really just needed App Engine, but were reinventing it with Compute Engine because they didn't know better. Others were trying to use Cloud Functions for the job of Cloud Run. Trust the docs and you'll prosper.

Simplified Smart WebApp development