I missed the functionality to globally toggle picture-in-picture directly from the keyboard.
So I created an applescript to toggle opening and closing.
Currently supported Applications: Safari, IINA
Shortcut: cmd ⌘ + ctrl ˄ + P
just an fyi – ⌘ + ` is actually the way to switch Safari window, so it wouldnt be good if someone was trying to switch window and accidentally triggers picture in picture
Oh, good you mention ⌘ + `. Yes, it's the default to switch between windows of the same application Move focus to next window. Changed it to ⌘ + § which it should've been in the first place. Karabiner Elements seem to have a bug here. (I use an UK Layout)