I'm having the same problem here but I just restored to a new machine with Catalina (10.15.6 -> 10.15.6) with a Time Machine backup.
Alfred 4 was working just fine on the other Mac but now, I'm having the same issue as above. I can see my clipboard history, I can hit return...nothing happens...but it is on the clipboard so I can command paste it. I've tried all different combinations of removing and adding permissions, restarting Alfred, the Mac. No avail.