Before, Free Look would accept background input by default, which means it was easy to accidentally move the camera while typing in another window. (This is because HotkeyScheduler::Run sets the input gate to `true` after it's copied the hotkey state, supposedly for other threads (though `SetInputGate` uses a `thread_local` variable so I'm not 100% sure that's correct) and for the GBA windows (which always accept unfocused input, presumably because they won't be focused normally).
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