PS: there’s also another functionality of Klipper that I use from time to time: you can make the whole “killring” appear, and choose the entry you want to paste with the mouse: as you click it it’s entered. This is also bound to a key (in my case S-w) and works no matter which window I’m in.

If you right-click on the Klipper tray icon, select “Configure…” and then “Shortcuts”, you can assign shortcuts to move back and forth in the kill ring, and to paste. I have assigned S-v for backwards and S-C-v for forward. Then the usual C-v will paste. The tray icon also shows you the current selection (and the ones above and below) in the killring, as you move through it.