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.
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.
If you're willing to share, is maintaining that modularization the plan going forward? I'm pretty happy to use and pay for this and deploy it to fly, but only as long as I'm not "locked in."