Thanks, DrMoishe Pippik, for the link to the Windows bug. Except that is the reverse problem, of how to enable slideshow.
In my case, our clever system admin noted that having two pictures selected, Windows "thinks" about a slideshow, logically.
As a programmer myself, this would make sense. Just think about it. Someone made a nice settings app for slideshows with all kinds of nifty features, and then thought, well, if you don't want a slideshow, you just install only one (1) picture. So the option for "picture" is just an extra menu option, without any extra software behind it.
@harrymc How did I install a different background wallpaper for each monitor? Well, the hard way is to use the Settings, Background app, which may or may not have a feature for this. The easy way, which I found on some windows forum, is to use File Explorer, by going to the folder with your wallpapers, select two pictures using the control key, go to the context menu with the right mouse button, select "Set as desktop background". That simple.
In most cases, this does not work exactly as you wished, one or both monitors can show the wrong image. Then, just right-click on a free place on one of the monitors, i.e., on one of the wallpapers, and select "Next desktop background".
However, this last tip also shows that "slideshow" is enabled. Which proves the theory of my system admin. The bottom line is that:
You cannot select a different wallpaper on each monitor and make this stick.
What you CAN do is set the slideshow interval to the maximum value of one day, to minimize the pain of having to deal with this Windows limitation.