It seems to only "search" the "suggested" list. Or whatever we wanna call it. The top list that get's autocompletion on the website search while you type.
Since the regular site search is disabled on the Itch app, I have to assume, this is intentional, and I can guess reasons, if that really is intentional.
Search is literal title search (and literal user name search, but the results are the games of those users). It might just be, that practically no one uses search to search for games that are not also on the suggested list. One just does not search an unknown and obscure game by it's title. One does "search" unknown games by tags. And the search bar does not search games by tags.
Or it is just broken for the app, and they removed it, because it only ever gets used by developers searching their own games.