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...