If I was sharing a GUI with coworkers I would use Zoom. If it was a terminal I would enable Multiuser in GNU Screen. If you mean remotely managing a windows server as its administrator then I would use RDP. Microsoft's RDP terminal server is integrated into their security controls and group policy.

My use case is closer to RDP, but as I understand it, you cannot host RDP through a firewall without Windows Server, which I don't have (plus, I don't have much interest in opening a port into my home network). I'm looking for something that is always enabled, so I can access a machine while it's unattended (so Zoom and the like are out, since there's a 1 hour limit and you need to click a link).

Maybe Chrome Remote Desktop? Or RDP, but using a VPN of some sort? I know there's a little-hassle tunnelling setup you can use a la WireGuard that's been on HN, but I can't remember the name

If this was a personal desktop then maybe something like Hamachi/Logmein would work.