Like I said in my original post, using the right click context menu doesn’t work either (Right Click, Paste).
I moved my .config, and .local directory out of the way, and it worked again for a while.
Then I started copying back in from the old config/local certain directories (nothing to do with KDE/Plasma, I did however copy back in gtk directories) and it broke again.
Edit: Klipper sees the copied item, but I just can’t paste it anywhere (with either keyboard shortcut SHIFT-CTRL-V for Konsole, or right context menu of paste in Konsole, or Kate, or any other application). It’s like Paste is disabled.