podman can't replace docker-compose. it can only replace docker. if you install podman-docker any docker command you run will be translated to a podman command. I think that should work when you run docker-compose as well.
Podman Desktop also offers to set the socket emulation and Docker compatibility up for you, if you like.
podman-compose will and it behaves more or less the same way but it's quite a neglected piece of software - lots of bugs, lots of open PRs.
A lot of people talk about quadlets or k8s as alternatives but I don't think these are generally good substitutes for compose.
> enable podman.socket (available as system and user unit)
Won't it make podman be daemon then if it'd be activated by socket?
Won't such a daemon be run as root then to be able to handle creation of networks/ports forwardings/multiple-users?
podman-compose[1] replaces docker-compose.
[1] https://docs.podman.io/en/latest/markdown/podman-compose.1.h...