How to keep graphic TTY session running at background

Using debian 12, kde 6 My intention is to use my pc as streaming platform for two, meaning that 2 game instances will run at once. First gaming session will run directly on the pc itself, and the second one, running at background, will be redirected to laptop to control the second game instance from there. Current configuration I got is 2 steam clients running at different kde sessions (TTYs) under different users. Second session is streaming to laptop via Steam Link. The problem is, after I launch the second session and switch back to the main session, the stream to steam-link-client-laptop stops immediately, meaning the session or steam process are freezing. Is there a way to keep 2 graphical TTY session running simultaneously?