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What would be the easiest way to position a component anywhere on the screen, so like an overlay, but not using Window or PopupView (which both behave differently from what I need)?
check out the PopupButton add-on from the directory. If you don't want the button part, see the source code on how it handles the overlay; that should give you some hints on building your own. The isOrHasChildOfPopup method does the detecting if a clicked element is inside the popup.