Do Firefox addons/browser extensions have the ability to trigger keyboard shortcuts?

On Firefox, there used to be a button that enabled Picture in Picture video. But I used some Firefox CSS theme and now it isn't there anymore. Now, i could try making an extension that does picture in picture for me but that's hard, instead I could try making an extension the presses the keybind Ctrl + Shift + ] for me so picture in picture triggers, can an extension do that or does it violate some security feature? See my overflow post for more info. For clarity, since some users didn't understand, The extension's icon (which typically appears at the top of the browser), when pressed, should

Question by jordanthejew on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.