My new phone is back to working. Wasted a whole day with this nonsense. My debugging mind says... software crashed (most probably the app I was using for the first time to listen to books), and the crash put a black screen, and stopped all other apps. Very hard crash, which wouldn’t even allow reset buttons. Plugging it in just prolonged the problem because it kept the crashed process alive. When I finally gave up on it and stashed it away in a bag, the crashed process used up the battery power, and then the phone was just dead, dead for lack of power. For some reason, late yesterday afternoon I was really angry about this failure and got the phone out of the trip bag (I was going to take it on a trip to a country with Apple stores), and pressed buttons. Ta-da... The dead battery icon showed. I charged it 100%, and it’s fine.
So... letting it DISCHARGE overnight may be the solution for this type of problem.