MacBook Pro won't recognize USB keyboard any more
Success!

After I posted this, I tried a few more keywords in my Googling and found this: How to map Caps Lock as a second Control Key on a Microsoft Natural Ergonomic Keyboard 4000?

And it turns out that uninstalling the Microsoft drivers (by running the programs in Applications/Utilities called "Intellitype Uninstaller" and "Intellipoint Uninstaller") did the trick.

I don't know why the Microsoft drivers worked fine for years and only broke last night, but my keyboard is now properly recognized as what it is and I didn't even need to adjust the setting in the "Modifier Keys" dialog in the Keyboard System Preferences: it remembered what it should be, and once again shows my keyboard as a "Natural® Ergonomic Keyboard 4000" and not just a generic "Keyboard".