I've found a more convenient workaround: the square does not appear at least on SDDM if the new session was started not from X but from a TTY. The command I use in TTY is
$ qdbus --system org.freedesktop.DisplayManager /org/freedesktop/DisplayManager/Seat0 org.freedesktop.DisplayManager.Seat.SwitchToGreeter
I've found a more convenient workaround: the square does not appear at least on SDDM if the new session was started not from X but from a TTY.
The command I use in TTY is
$ qdbus --system org.freedesktop .DisplayManager /org/freedeskto p/DisplayManage r/Seat0 org.freedesktop .DisplayManager .Seat.SwitchToG reeter