Took me a minute to find out what was going on there...those look to be mechanically activated hydraulic calipers. I've never seen something like that before, but those XT calipers are definitely not that. They look to be maybe a bit easier than full hydraulic to install, but I have no idea how they would perform.
Are your cables externally routed? If so, I'd just go full hydraulic, as you can buy them with the lines already filled and attached, like this:
https://www.thebikeshop.com/product/...r-374616-1.htm
Then you replace your levers and calipers. You may also want to replace the rotors, as some pad materials are compatible with some rotor types, so you'd ant to see what is imprinted on the rotor, and make sure it matches. You can mix them, but brake performance is supposed to suffer a bit.
EDIT: Sorry, didn't listen to the guy at the start, and the issues with the switch in the lever. So not so straight forward. You would have to find those hydraulic calipers. Might be the only option.