How can I pause PotPlayer reliably using the "Space" hotkey, regardless of current window?

You can assign a hotkey to pause/play globally, regardless of the open window and it works everywhere. Whether that is a solution to your problem is up to you, since there is no option to assign hotkeys that work only in PotPlayer windows (either the main player or playlist window).

For a global hotkey, in preferences (F5), go to General > Keyboard. Add a hotkey (for example, Ctrl + space), assigning it to playback: play/pause. Make sure that you check global (as in the picture below).

Global hotkey for playback in PotPlayer