Having read the description of that adapter, looked at the diagrams, and read the reviews I'm pretty sure it doesn't allow you to run a USB device off an ethernet port, except apparently on some ADSL modems that have a combined ethernet + USB RJ45 socket.

I see you can get 'mini PCs' which are somewhat equivalent to a RaspberryPi and run Windows 11. Mostly ~£150 but there's one on Amazon for £80 - brand 'PELADN'. It's unobtrusive, but you'd have to work out how to access it. Remote Windows Desktop, if there is such a thing?