Fix flyout menu behavior when new sidebar is in "peek" mode

Problem to solve

In #415343 (closed) we reintroduce the "flyout" menus for our redesigned sidebar (behind a feature flag). The problem is, that while the sidebar is in "peek" mode, it auto-closes as soon as the mouse pointer moves away from it. It doesn't yet consider the state where a flyout is visible and the user moves from the "peek" sidebar over to the open flyout menu. But the flyout menu disappears together with the sidebar, making it close to impossible to click a item in it to navigate.