There are still edge cases, but things have improved rapidly the last year or so, to the point that most docker-compose.yaml files can be run unmodified with podman.

I have however moved away from docker-compose in favor of running containers and pods as systemd services, which I really like. If you want to try it, make sure your distro has a reasonably new bersion of Podman, at least v4.4 ot newer. Debian stable has an older version, so I had to use the testing repos to get quadlets working.