If the search results Display is on the Grid when creating a live search, the Live search results option in the query loop does not work as expected.
In fact, as you know, this option (Live search results) behaves in such a way that the search results section is displayed only when the search box is active. But if the search result is Grid, this behavior will not work. I hope the following screenshot is useful in replicating the bug.
sadly, I was unable to replicate the issue you mentioned. Please check my screenshot below where you can see that the result section is displayed as a grid.
Please watch the video below. When the block is Grid, clicking on the surrounding environment does not hide the search results section. But when I change it to flex, the problem is solved.