The tools I am using to develop QAP does not allow to add a scroll bar to a dialog box list when it contains multiple images per row as this one. This is why the Manage Icons window is presenting the icons page by page.
Each page contains as many icons as possible according to the size of your screen. The number of rows displayed in each page is calculated based on the screen size reported by Windows. If, for any reason, Windows returns an incorrect size value to QAP or if QAP misinterprets this info (which seems to be the case when screen scaling is active), the window could be too small or, more frequently, too large. This could make the window unusable because the Previous, Next and Close buttons could be "outside" of the screen.
The solution to this is to manually set the number of rows of this window. To do it, open the Options dialog box, Menu tab, and enter a small number of rows in the Manage Icons window row zone. After testing it, increase the value up to the maximum that works on your screen.
More info about managing icons: Can I manage all my menu icons in one screen?