I know this must be possible, as its the default on Wikipedia links, but I've been digging through https://doc.wikimedia.org/oojs-ui/master/js/#!/api looking for an on hover event trigger, and I didn't see one. How can I make a button (or a link, doesn't really matter so long as it can redirect) that triggers a popup when you hover over it?
Topic on Talk:OOUI/Widgets/Popups
We don't provide this behaviour in the library, for the obvious accessibility and mobile problems. You could build one, but be careful in it use. The functionality to which you refer is the Page Previews tool. The code for that is located at https://gerrit.wikimedia.org/r/plugins/gitiles/mediawiki/extensions/Popups/+/master but is rather labyrinthine, and doesn't use this library but instead is manual code styled to look like it.
@Reinischmax On top of @Jdforrester (WMF)'s answer, there has been T161403 with a similar request for the library's PopupButtonWidget. If you wish so, please share your use case for documentation and development planning purposes.