Docker docs:
Docker routes container traffic in the nat table, which means that packets are diverted before it reaches the INPUT and OUTPUT chains that ufw uses. Packets are routed before the firewall rules can be applied, effectively ignoring your firewall configuration.
cockpit has a podman/container extension you might like.
It’s okay for simple things, but too simple for anything beyond that, IMO. One important issue is that unlike with Portainer you can’t edit the container in any way without deleting it and configuring it again, which is quite annoying if you just want to change 1 environment variable (GH Issue). Perhaps they will add a quadlet config tool to cockpit sometime in the future.