I just tried it (Win 10, Cubase pro 15.0.21) and can’t confirm the problem: Double-clicking a MIDI part in the Arranger window opens the Key Editor on my second monitor and it has focus. All keyboard commands are immediately reflected in the Key Editor.
Same here as raino and Johnny. I’m Windows 10 but use 4 displays. No matter where I place the Key Editor to open, it always retains focus when opening.
Did you try checking this with Safe Mode and disable user preferences?