The apps screen closes when I click on the icon again, launch an app, or if I click in the left or the (most of the time invisible) right strip next to the icons. It should also close if I click basically anywhere on the background, in particular when I click in the area not occupied by the icons.

I suggest however, that we exempt the tiny area between the tiles from this as else and badly placed click causes confusion: it would feel similar to an app launch in that the apps screen is closed, but the app that then re-appears would be an already open one and not the one you though you'd clicked on.