I’ve always found GCP documentation to be absolute trash, if you can use AWS Lambda do it, our indexing service/data portal runs off of it it works very well, the integration with CloudWatch insights makes logging pretty straightforward.

I believe Datadog and New Relic have integrations to monitor Google Cloud functions. You can also monitor through Cloud Monitoring if I am not wrong.

Can you use Health-Checks (under the Compute Engine drop down) to monitor Cloud Run? I use them with Instance Groups for deploying docker containers.