Further details: mouse cursor is briefly visible just prior to the black (login) screen. GDM does show up on the display, but in too big a resolution, so that I only get some of the grey background visible on screen and still have to log in blindly.
It occurred to me that with lightdm, the symptom appears as I would expect if it failed to do monitor detection properly and thinks it’s displaying the login screen on the (broken) internal display only. Well, apart from the funky ”login screen desktop background” phenomenon (which could be a separate issue though).
(Just to be clear: this same combination of broken internal + working external display did display the login screen correctly on the external one in Precise.)