It's easy enough to integrate with Google Cloud Run.

I run a mix; some apps are pure Firebase and Functions. Some run Cloud Run serverless containers connected to Supabase upstream and Pg container locally.

Firebase is quite flexible as a chunk of it is a facade for Google Cloud services (storage, auth API, CDN, Cloud Run).

Very flexible model of upscaling services progressively. Functions -> Cloud Run -> GKE Autopilot -> GKE