Shortly after my post, I decided to see how the MS team responded directly. Using HELP, I contacted the MS person available to all of us (free of charge) who own a legal copy of Windows 11. She quickly fixed both my machines.
- She began by downloading a MediaCreationToolW11:
Download Windows 11 (microsoft.com)
- She launched it and opted for #3:
Download Windows 11 Disk Image (ISO)
- She then opened the disk image and ran the installation program which limited itself to reinstalling all updates including the current one. There was a lengthy installation both before and during the reboot.
- Reboot and run Windows update one last time.
NOTE: None of my apps were removed or lost their settings. No documents, etc. were removed.
Problem solved. It took about 3 hours. Installing all updates rather than simply reinstalling Windows seems to be much more machine intensive. If you try this, do so with care.
PS: Notice that this did not explain why the problem existed to begin with, nor am I convinced it won't occur again. If so, we can continue looking for common factors: I would prefer a quick update to a long, long repair.