I'd recommend Barrier over wireless/Bluetooth switching.
https://github.com/debauchee/barrier
It's in the package manager too. You just glide your mouse across to the decks display as though it were a second screen and your keyboard and mouse work seamlessly there. Alternatively you can switch with a keyboard shortcut.
Thanks! I might have already known this, it does ring a bell, but last I dabbled Barrier was maintained.