My understanding of Fly Postgres is they put a lot into the tools to orchestrate, but there is not centralized monitoring and in the event of a failure it is up to you to realize and remediate.
Disclaimer: Was part of the team that built Heroku Postgres, and know the Fly team pretty well but don't personally use Fly Postgres so it's my understanding from the team. We've had a number of customers leverage Crunchy Bridge (build by a lot of the original Heroku Postgres team) use us for the managed Postgres connected to fly.io via Tailscale.