Thanks for the tip! I deactivated all plugins and reactivated them again one by one. The culprit was a plugin called “Use Google Libraries” (which makes sense because the toggles use js/jquery to work — the correct library must have been being overridden). Whew!
This topic can be deleted. The issue was apparently fixed by re-installing WordPress core.
Thank you – when I first tried the clean-out, it didn’t appear anything had changed (even after clearing the cache), but a few days later I have checked again and it seems to have worked. Thanks again!