This isn't (completely) true. I found podman-compose to be a more or less drop-in replacement for docker-compose. I know that in the past support was patchy, but things are rather good now.
e: from the manpage:
"podman compose is a thin wrapper around an external compose provider such as docker-compose or podman-compose. This means that podman compose is executing another tool that implements the compose functionality but sets up the environment in a way to let the compose provider communicate transparently with the local Podman socket. The specified options as well as the command and argument are passed directly to the compose provider."
this is literally what manpage you quoted says too