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You could also achieve this with pure X server and several system users: X controls your display and inputs (kb/mouse), and you let different X clients from different system users display on that server (eg. set the DISPLAY env var properly, configure X server permissions with xhost utility).

Then, you use a configurable tiling manager to control which windows go where (I am sure you can even go by the user somehow, but maybe you'll need to "decorate" the client run with an env var too).

what i do for work is very close to what you want and its pretty easy to achieve with using lightdm and the dm-tool with the add-nested-seat command. It will start a new Xephyr X server local to your current user and attach the session manager to it. from there you just login and have the second user session in a window just like you wanted... however, i did not get clipboard sharing to work but i actually like this extra bit of isolation.... its not even hackish and performance is exactly as native because it is... its a bit harder to get sound working concurrently, but not impossible, although i never really tried. However, i use pipewires pulseaudio interface to stream audio to a remote AV receiver in the room and this should work fine in the second user session too, although as said i never bothered to try...

Sway has multiseat, maybe it would be a match for your use-case, check manual for sway-input.