I know GCP has "functions" (which is terrible to search for ironically), but haven't run across any other 1:1 equivalents. What are the thorny/sticky parts to watch out for on each, and are functions (or any others) at the same level?
AWS Lambda is quite a bit ahead of GCP functions. However, it doesn't look like Google is really going as hard as AWS is to improve upon that product. Google is much more focused on container orchestration with Kubernetes. I believe they have the upper hand in that arena.
app engine was ahead of its time
Lambda has a lot of baggage that you have to include to deploy a function. Definitely as not as refined or sexy as the competition, but it works.
VPCs, subnets, and KMS just to get going is for sure an interface only a developer could love.
Azure functions