Since I've disabled that option in KDE Connect I've not seen the pop-up once (been a couple of days).
It makes sense because I think KDE Connect is regularly copying stuff to the clipboard from the connected computer. A lot of the time it will be the same data and whereas Android 11 never reported it, Android 12 obviously does.
So it's not an Android issue as such (although why _would_ it report that a needless copy to clipboard operation has been performed? It would just be an annoyance anyway!), I think KDE Connect needs to change to a check before copying to the clipboard.