Is it possible to use Firebase to direct requests to a Cloud Run container which is in another project

So on the official firebase documentation it looks pretty straightforward to see that we can direct requests to our Cloud Run via proxy.

https://firebase.google.com/docs/hosting/full-config#rewrite-cloud-run-container

So its says if you add your cloud run's serviceId it will be done:

"hosting": {
 // ...

 // Directs all requests from the page `/helloworld` to trigger and run a `helloworld` container
 "rewrites": [ {
   "source": "/helloworld",
   "run": {
     "serviceId": "helloworld",  // "service name" (from when you deployed the container image)
     "region": "us-central1"  // optional (if omitted, default is us-central1)
   }
 } ]
}

However this does not cover my problem where you have different projects so you cannot directly give the container image/ service name. They are on the same account but in different projects.

I tried giving the direct destination:

    "rewrites": [
      {
        "source": "/api/**",
        "destination": "MY-CLOUD-RUN-APP-URL>/api/**"
      },
      {
        "source": "**",
        "destination": "/index.html"
      }

However this didnt solve my problem.

This is not possible. The configured Cloud Run instances must be in the same project as Firebase Hosting.

You could possibly set up a Cloud Run container to forward/proxy HTTP requests to another publicly accessible Cloud Run instance in another project (or any other HTTP service for that matter).