Start screen blocks popup interactivity

The bottom right looks like the thing to click away first (similar to cookie popup on websites), but that didn't seem to do anything. That was confusing for a few seconds. And then I closed the start screen popup first.

Reproduce the interaction between the start screen popup and the bottom-right control, noting which element receives input and in what order the popups close. The issue does not name a file, test, or entry point, so first locate the start-screen UI implementation; done means the apparent dismissal control behaves clearly and popup interaction is no longer blocked.

Written by the indexing model from the issue text.