To get away from TeamViewer for managing remote clients, I have now deployed a RustDesk server instance for testing purposes.
Hopefully everything will work as desired so that I can fully switch to RustDesk in the future and get rid of another external solution.
One limitation that is currently still relevant for Linux is that there is no Wayland support yet.
But that doesn’t bother me at the moment, since I probably only use Linux for control, and here all devices still work with X11.