@khuezy is right about IPv6, and it looks like you’ve maybe fixed that for the management port (15672) but not for the main port (5672).
A quick glance at the RabbitMQ networking documentation suggests the following instead:
listeners.tcp.default = :::5672
You can see what really is listening on your machine at present by combining SSH with ss. (Those are Debian instructions, but Alpine should have something similar.)
Aside: It’d be wise to remove all of the [[services]] blocks and all the public IP addresses, since those are exposing your message queue to the outside world unnecessarily. The warning that you quoted earlier about fly-proxy is a red herring; it’s referring to a different Fly Proxy (unfortunately). The one that you’re using (i.e., the flyctl subcommand) is oblivious to [[services]].