Podman works with Docker Compose enough to run stuff I've had to deal with at work and home. I prefer to use the podman-compose script usually, since it does offer some small advantages when using Podman. That said, even with the podman-compose script, I ran into an issue where some syntax somewhere needed to be adjusted for Podman; I can't remember exactly what and I don't have access to the repository to check, but it was a security-related flag, and it was fixed in master at some point, I believe.
Getting Podman to run CUDA/Nvidia workloads was a bit more challenging, but that can also be done.
Docker Compose works fine with Rancher Desktop. You can use it with Podman on Linux too, you just need to enable the socket since normally Podman does without - I'd imagine there's some way to enable this on Podman desktop too.
For Rancher Desktop, Docker Compose works with Rancher Desktop when you choose dockerd (moby). If you choose to use straight containerd (with nerdctl as a CLI) than compose isn't going to work.
Getting Podman to run CUDA/Nvidia workloads was a bit more challenging, but that can also be done.