Hi, do you mean a CT or Host shell? I mean there's no actual minimize and depending on what it behaves a bit different.
For the Proxmox VE node shells you'll get a new shell spawned if you reconnect or open a new session, if you need continuity here use a terminal multiplexer like "tmux" or "screen".
For Container it depens on your CTs settings, if it uses the default "tty" mode or the "/dev/console" mode you connect to something more persistent, and once you reconnect the previous state is still there, even though it's maybe out of screen (hit CTRL + L or the like to clear it). If you select the "shell" mode it should be the same behaviour as you see with PVE nodes.
For VMs you normally just connect to it's display, so depending on what runs in the VM it behaves accordingly, but normally the shell/viewer state stays.
You can open a shell in a new browser tab or window for longer running sessions, and as said, a terminal multiplexer may make it more easier - as this could even be picked up again if you (re)connect over something completely different, like SSH.