There are no errors in Xorg log files. I have already included before the error messages I got from the RS232 cable. Those were assertion errors doing some CSS bezier effect (transition ease-in probably).
In my current installation the default GNOME DE was selected. Now I tried installing LXDE via 'apt install lxde task-lxde-desktop'. I selected lightdm for display manager then rebooted. I got the blinking underscore again. I rebooted in safe mode and switched back to gdm3 via 'dpkg-reconfigure gdm3'. Now it works again and I can even select LXDE via the gear icon and I can log into LXDE and it works OK. So it seems to be that it has to be something with lightdm.