When you go to the activeties menu and you start typing, the searches are shown. So far so good.

But the left-right arrows only work to go left or right in your search phrase, and the up and down arrows are used to go left and right in the icon view.

I believe this could be done better.

The cursor is at the end of the search phrase, than there is no point in going right, so the icon view could become active when you press the right key, so that you are able to walk through the icons in 2D mode: down means down, up is up ...

When you arrive at the top row of the icon part and press up, you should go back to the search phrase, when you arrive at the left column and press left, you should also go back to the search phrase.

I believe this will be a lot more intuitive and quicker than using up-down for the icon view and let-right for the search phrase. But it's up to you if you want to implement it.