Phoenix creator here. I'm happy to answer any questions about this! Also worth noting that phoenix.new is a global Elixir cluster that spans the planet. If you sign up in Australia, you get an IDE and agent placed in Sydney.
How tightly coupled to Fly.io are generated apps?
Everything starts as a stock phx.new app which use sqlite by default. Nothing is specific to fly. You should be able to copy the git clone url, paste, cd && mix deps.get && mix phx.server locally and the app will just work.