The mediawiki.Title module has an exists() method which sounds like it would check for existence, but actually it just returns null. It is probably meant as a standard place to store title existence information that was fetched manually, or maybe it's just an unfinished feature... in any case, it should be documented clearly that it's just a boolean flag store, without any lookup logic.
Currently exists can only retrieve the value if it already knows it, see also:
https://doc.wikimedia.org/mediawiki-core/master/js/#!/api/mw.Title-static-property-exist
https://doc.wikimedia.org/mediawiki-core/master/js/#!/api/mw.Title-method-exists1
https://doc.wikimedia.org/mediawiki-core/master/js/#!/api/mw.Title-static-method-exists1