Get user's email in google cloud run application

Question

I have an application which runs on a service in google cloud run. I use Identity-Aware Proxy (IAP) to ensure that only specific users can login to the app. I want that part of the application will only be visible to some of the users, and in order to do that I want to know who is the user that is currently trying to run something with the application. How can I do that?

I tried to do:

credentials = service_account.Credentials.from_service_account_file(
            file,
            scopes=[
                "https://www.googleapis.com/auth/cloud-platform",
                "https://www.googleapis.com/auth/userinfo.email",
                "https://www.googleapis.com/auth/userinfo.profile",
            ],
        )
        auth_req = google.auth.transport.requests.Request()
        credentials.refresh(auth_req)
        token = credentials.token
        headers = {
            "Authorization": f"Bearer {token}",
            "Content-Type": "application/json",
        }
        url = "https://www.googleapis.com/oauth2/v3/userinfo"
        response = py_requests.get(url=url, headers=headers).json()

The problem is that I'm sending the request to the wrong place (i.e not using the right file).

From what I understand, I want to send a request to the IAP and ask for the user email.

Thank you!