It has worked in the past and showed the option on the drop down within either the lock screen or background (one, but not both). Right now my background dropdown has 4 options - picture (which it is set on now and shows a couple word description of what the picture is along with the photographers name), Solid color, Slideshow or Windows Spotlight - which has doesn't seem to change but does have "learn about this picture" that when clicked, brings me to a bing page. I would be ok to have spotlight on my lockscreen if it also has the little info icon (which mine currently does not have).
As for the lock screen, it has 3 options within the dropdown - Picture, Slideshow or Windows Spotlight (which it is set to and for some reason today it finally changed from the flamingos to a tower or castle in the distance surrounded by trees - but it has no description or option to see what/where the picture is).
This is frustrating but really trivial. It is taking up too much time for something that isn't important but I really like the old way with Windows spotlight that automatically changed pictures each day and had a little icon on the screen which, when you hovered over it, it gave a brief description of the photo or you could click on it and a new window would open with more detailed info of the photo.
I am not good with the details of computers and what's going on in the background. I just know surface level stuff/basic stuff so when you say "If you keep switching between your Microsoft account and a local account and then back to your Microsoft account, eventually the image will change. It doesn't necessarily need to go through OneDrive". I don't really understand about the switching back and forth part. I just log into my computer each morning but we do use One Drive. I actually just thought that One Drive was what enabled us to be cloud based an no longer need a server. Ugh, sorry for sounding so dumb.