podman-compose is "mostly" compatible. I "plain" podman at work, but there we just have a bunch of shell scripts that spin up/down/build containers. For regular dev work, it's fine.

For personal stuff, I've been experimenting with podman's Kubernetes files: https://docs.podman.io/en/latest/markdown/podman-kube.1.html. Which, IMO, "feel" like docker-compose the most. You can run services via "podman kube play ..." and install them via quadlet install too.