The Itch app cannot search at all. I do not know why. Even the regular search box is not displayed on page.
and even there you have to be lucky to find the game
That's probably why. Because it is not reliable to begin with. Search results are capped and it is literal title search. Generic titles are very hard to find by literal search. There's at least 10 different games by the exact title Do Not Disturb.
The "search" box in the app only searches the top games. It might lower user experience, if all the copy cats would be displayed along with the thing they imitated.