loginctl enable-linger USER
(run once, as root) should cause USER's podmansh container to start as soon as the system enters multi-user mode, independent of USER's login sessions, allowing persistent daemons, including those necessary for job scheduling, namely…Ordinarily, users can create systemd timer units[4] to schedule at- and cron-style jobs; I assume you need to run a systemd instance inside each user's podmansh container to allow users to create systemd units in the present containerized context (running systemd inside a container is explicitly supported by podman[5]).
If your users don't like systemd, you can also run traditional atd/crond daemons in user containers.
[1] https://www.freedesktop.org/software/systemd/man/systemd.gen...
(This is the same mechanism that, e.g., automatically creates systemd mount units for mounts defined in /etc/fstab.)
[2] https://docs.podman.io/en/latest/markdown/podman-systemd.uni...
[3] https://github.com/containers/podman/blob/6ab38e55e733e70c95...
[4] https://www.freedesktop.org/software/systemd/man/systemd.tim...
[5] https://docs.podman.io/en/latest/markdown/podman-run.1.html#...