From what I understand, KVM setup is what is used. In the olden days it used to be a keyboard and monitor in every rack with a switch to connect to all the machines in the rack. Nowadays I’m sure it is more software than hardware but same principle. A home setup would be a laptop form factor device that can take in different video inputs and has a keyboard. A mouse wouldn’t even be required but I guess wouldn’t be hard to add. It would need a battery for the monitor but really would need no brains at all.

Another option would be a computer that can do video in and act as a USB HID for the keyboard/mouse but then allow you to connect to it via VNC. This really could be amazing if you could just plug in two cables and then go to your laptop to connect to it.