Emulator Suite warning about default project ID when GCLOUD_PROJECT is unset in CI tests

I'm setting up integration tests against the Firebase Emulator Suite (Firestore and Auth) as part of a CI pipeline. The tests never touch production, and the emulators start correctly, but the emulator logs a warning that no project ID was provided and that it is falling back to a default project ID.

My concern is determinism: some of my test helpers construct Firestore references using a hardcoded project ID, while the emulator itself may be operating under its own fallback ID when GCLOUD_PROJECT is unset. I want to understand whether this mismatch can cause subtle failures — for example, connections silently targeting a different project namespace than the one my test fixtures assume — and whether the fallback ID is stable across emulator versions and environments.

Assume a recent Emulator Suite release and the modular JavaScript SDK with connectFirestoreEmulator.

Specifically:

• Does the emulator's default project ID remain constant across versions, or can it change and break tests that implicitly depend on it?
• Is setting GCLOUD_PROJECT (or passing the project ID to initializeApp) sufficient to make the emulator and client agree on the project namespace?
• Are there documented cases where a project ID mismatch causes silent misbehavior rather than an explicit connection error?