If I click on its browser window or playlist window before minimizing, the "space" hotkey does not pause it when I click on it again in the taskbar and press the "space" hotkey. It only works when I clicked on the main PotPlayer window prior to minimizing it.
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).