It seems that the XScreenSaver hacks that grab the desktop are no longer able to do that on macOS 11. They just get the background image, not a screenshot.
Is there something I can put in the plist to request such access? On iOS you can use things like NSPhotoLibraryUsageDescription to make it pop up a dialog requesting access to photos. Does macOS have something like that? (Though even if it did, I'll bet it would only work for apps, not .saver bundles... Sigh...)
It turns out that adding "/System/Library/Frameworks/ScreenSaver.framework/PlugIns/legacyScreenSaver.appex" to "System Preferences / Security / Privacy / Screen Recording" fixes it -- but is there some shell command that my installer can use to do that automatically?
(Oddly, after adding it manually, it does not show up in the list. But the savers are now able to grab the screen.)