You are correct - they will vary per region. Which adds an extra complication.
You also can’t get a static outbound IP (e.g to use in an RDS security group) from Fly. As you’ve seen, the IP you are shown is for incoming connections. Like for a DNS A/AAAA record to point a custom domain at your app.
You have probably already seen this thread but if you scroll up and down it you may see some ideas, like: