I have the same problem and it happened twice on two different websites. In both cases it showed at first, but after menu was deleted, search in menu was gone after menu recreation, plugin reinstallation and and its reactivation.

The trigger seem to be a deletion of the menu, once you re-do the activation process for a menu created from scratch (since previous, “main”, or “first” menu was deleted by mistake, or bug from another plugin), you can’t make the search element to show up in menu. It simply is not appearing, as if it was blocked, or bugged, or missing trigger to show up.

I did all the steps recommended in the installation instructions.