I usually also use Cloud Run for running my containers. But I use Cloud Build instead of GH Actions. I'm curious, what's your reasoning? I prefer my repository to just hold code and run build actions close to where it's deployed.
For me, I had use GH Actions before so it was pretty quick to get up and running. I am sure it was not that much more effort to use a cloud build tool in GCP or AWS but honestly don't see that much of a pro/con.
I guess in my view depending on GH actions means if it's down I'm blocked but if it's just a repo I can always point my build system to a different one. I have never experienced GCP being down and would bet it has better overall uptime than GH...