Find in Document in split view

If I open a PDF and split view (horizontally or vertically) and then click Cmd + F (with focus set on the "splitted" view, not the main one), nothing happens. I have to click on the "Find in Document" icon explicitly.

And it seems I'm unable to search on the "splitted" view. Only on the main one.

Maybe it'd be nice if the Find feature worked on the view that is on Focus?
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