I hadn't thought about this enough, because this would only be possible with Logitech software and would not be suitable for booting. If several computers were connected to such USB sticks, the mouse would not know which computer to connect to when booting, or would move the mouse on all computers. The same problem would occur with the keyboard.

Just take a mouse from the MX series, then it will work for sure.

Works with the current Logitech dongle, which is included with most devices.