Starting the teamviewer daemon from Konsole on :0 (ctrl-alt-F1) asks for password authentication in a usual popup window. Entering the password to allow the teamviewer daemon to run also starts a fully functional X with KDE/plasma on :1 (ctrl-alt-F7, where it would normally be), in parallel. Widgets, window decoration, desktop wallpaper, screen locker, splash screen: everything works.
OK, this is truly bizarre:
Starting the teamviewer daemon from Konsole on :0 (ctrl-alt-F1) asks for password authentication in a usual popup window. Entering the password to allow the teamviewer daemon to run also starts a fully functional X with KDE/plasma on :1 (ctrl-alt-F7, where it would normally be), in parallel. Widgets, window decoration, desktop wallpaper, screen locker, splash screen: everything works.