I find it fascinating how, right after there is an OS upgrade--and thousands are experiencing the same problem--Apple will assert that it is something other than the OS upgrade. It's not a freaking hardware issue. It happened the very morning after I was automatically upgraded to iOS 17.5.1.
Now, for those of you experiencing the same thing, I can share that--although the Face ID setup just wouldn't work no matter how many times I tried it and no matter how many times I restarted my phone--it just did now, later in the day, approximately the 8th time I tried it. So I guess: just keep trying.