How to add the allUsers member in cloud run using Terraform

I would like to add the allUsers member to a google_cloud_run_service with the Cloud Run Invoker role automatically using Terraform.

To get around this:

Only authenticated invocations are allowed for this service. To allow unauthenticated invocations, add "allUsers" as a member and assign it the "Cloud Run invoker" role.

I don't have any issue adding the allUsers member manually and setting the role to Cloud Run Invoker.

But I was hoping that this could be done with Terraform.

I tried the following:

data "google_iam_policy" "noauth" {
  binding {
    role = "roles/run.invoker"
    members = [
      "allUsers",
    ]
  }
}
# Enable public access on Cloud Run service
resource "google_cloud_run_service_iam_policy" "noauth" {
  location = google_cloud_run_service.default.location
  project = google_cloud_run_service.default.project
  service = google_cloud_run_service.default.name
  policy_data = data.google_iam_policy.noauth.policy_data
}

But it does not seem to create the allUsers member after applying terraform plan and terraform apply.

Update:

main.tf

terraform {
  required_version = "= 0.14.7"
  backend "gcs" {
    bucket = "mybucket-terraform-test"
    prefix = "backend"
  }
  required_providers {
    google = {
      source  = "hashicorp/google"
      version = "~> 3.42.0"
    }
  }
}

foo.tf

resource "google_service_account" "service_account" {
  account_id   = "project_name-cloudrun"
}

resource "google_service_account_iam_binding" "admin-account-iam" {
  service_account_id = google_service_account.service_account.name
  role               = "roles/iam.serviceAccountUser"

  members = [
    "user:user@myorg.com",
  ]
}

resource "google_cloud_run_service" "default" {
  name     = "myproject-backend"
  location = "us-central1"

  template {
    spec {
      service_account_name = "myproject-cloudrun@myproject-dev.iam.gserviceaccount.com"
      containers {
        image = "us.gcr.io/myproject-dev/myproject/myproject-backend@sha256:abc123"
      }
    }
  }
}

## not working as expected ##

data "google_iam_policy" "noauth" {
  binding {
    role = "roles/run.invoker"
    members = [
      "allUsers",
    ]
  }
}

resource "google_cloud_run_service_iam_policy" "noauth" {
  location    = google_cloud_run_service.default.location
  project     = google_cloud_run_service.default.project
  service     = google_cloud_run_service.default.name
  policy_data = data.google_iam_policy.noauth.policy_data
}

##