Podman [supports][1] `docker-compose` now. Just set `DOCKER_HOST` to the path of your Podman socket after activating the service, and it should just work (unless you use Swarm, which is not supported).
It's worth noting for others that (it appears from a quick read, I haven't actually used this yet), the compromise for gaining the "docker-compose" superpower is that you will have to run a podman service (Daemon). This comes counter to some (not all) of the benefits I mentioned above, but is a necessary compromise if one wants the power of compose style orchestration; that is, that there must be some deamon to manage it.
This is not authoritative, I may be mistaken, but this is my educated guess based on a quick read and my knowledge of Docker et al.
It should be said that I was mixing that with non-root podman (although that should be a supported usage).
I went back to podman-compose.
Dunno