You're correct! The tool stops short of migrating the database from Heroku to Fly. I'm actually going to start working on this soon. Here's what that will look like:
1. A doc will appear at https://fly.io/docs/rails/ that walks through how to move over a Heroku app, including the database. I'm going to start drafting this next week since I have a few SaaS apps running on Heroku that I want to move over.
2. If the docs are complicated and have lots of steps, I'll look into automating most of this process. I don't think I'll be able to 100% migrate Heroku apps to Fly without any intervention, but I do think moving over the app code, ENV vars, and database would be a pretty big win.