podman does not autostart containers after boot. You have to manually start them, or write a start script. Or create a systemd unit for each of them.

I have not yet tried podman, but I know that podman-compose used to have an option to generate systemd units for your pods: https://docs.podman.io/en/latest/markdown/podman-generate-systemd.1.html

Still, that option has been deprecated in favour of Podman Quadlet https://docs.podman.io/en/latest/markdown/podman-systemd.unit.5.html