As a huge fan of podman this is definitely one of my disappointments. In the event that you're still struggling with this, the answer is using a --user systemd quadlet. You'll need to use machinectl (machinectl shell <user>@.host) for systemd commands to work, and you'll want to enable linger for that user.

One thing which just occurred to me, maybe it's possible to have a [container] and a [service].user in a quadlet?