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Hey there; I will take a swing at answering this. So firstly it’s worth noting I am mostly guessing here based on my GCP Cloud Run knowledge. 

Cloud Run health checks are currently Pre-GA. Which means they “may not” have full Pulumi support yet. This would be because it’s possible Google are yet to enable the specifics in the API discovery service that Pulumi would need to activate http path changing. 

It’s possible you could try referencing the way that the official GCP docs recommended setting up the health check path… 

<https://cloud.google.com/run/docs/configuring/healthchecks|https://cloud.google.com/run/docs/configuring/healthchecks>