The segment I copied was just long enough that it overflowed my chat window so I had no idea the insertion was even there and I sent it as-is.
The recipient called me about two minutes later and said "hey, I think you've been hacked - you just sent me a CBD oil advertisement."
So yeah, I'd love to see user agents address this. If I push a copy button (like github's clone repo button) then fine, I'm at the mercy of their javascript. But if I copy via ctrl-C or a right click menu, it should not not let the page interfere.