Podman has added full docker-compose support, and in fact even the docker binary works with it. Rootfull works as of v3.0.0, rootless was added in 3.2.0. Rootless can be a bit buggy, but I believe they polished a lot of the issues for 3.3.0.
Because they've re-implemented the docker api, it can actually work with any tool that uses docker's API.