Thx for your answer!
Since I asked, I’ve stumbled over document.execCommand as well, implemented it and can say: You are right in your assumption that “paste” is locked down (which is a problem out of scope of prosemirror).
I was hoping there is some kind of “weird trick” that solves my problem, but no luck it seems.
Currently I’m looking into manifest.json. Maybe I can request permission for “clipboardRead”…