The podman kube support? It provides similar functionality as docker-compose, using a yaml file which is a subset of the Kubernetes pod definition syntax.
Then you can just create a few line systemd unit definition, and it integrates as a normal systemd unit, with logs visible via journalctl etc.
This seems to be the way.
Short of weeding through the docs, I found the "Play with Kube using Podman" talk on DevConfs YouTube channel helpful.