This is a silly one, and I know there exist keyboard shortcuts, but I don't use them too much.
Perhaps this behaviour is due to some reason which I ignore, or simply was forgotten
When the Quicksearch textbox already contains some text, mouse right click is allowed and Cut/Copy/Paste options appear, some of them enabled or disabled as it should be.
But when it is empty, right click doesn't work, so if I have something to Paste, I can't do it directly.
As you wrote you can use Ctrl + V to paste the text.
The mouse shortcut doesn't work because of the hint text that hides the actual text field. I will check whether there is a simple solution for this.