The problem with making this work, IIRC, is that Docker Compose doesn't actually "compose" Docker commands, but instead _re-implements_ a bunch of functionality itself through its Python libraries. So you'd actually need to bring your own CLI-compatible Docker Compose implementation for Podman rather than just making your Docker replacement compatible.
In addition to the sibling comment (which mentions that you can use the original docker-compose) such a CLI-compatible reimplementation also exists [0]. It's not always a 100% drop-in replacement, but gets you pretty far in my experience.