Overall the integration story between podman and systemd is way, way better than with Docker. And that's in both directions, from using the host's systemd to start and manage containers, but also for running systemd within podman containers.
I would definitely expect that given the history of systemd and docker. IIRC difficulty Red Hat team had with integrating systemd and docker was one of the reasons why they started Podman rather than continuing to push everything upstream to docker. The docker team didn't want docker to have to accommodate systemd and refused some contributions that were important for a good integration.*
*There's still some bad blood out there about it, so I just wanted to make explicit that I'm not making a value judgment on docker's refusal. I'm not educated enough on the details to make a fair judgment. Sometimes you have to say "no" to features to protect your product.