No uncoupling membrane under that tile?? Yikes

Edit: you said Ditra isn’t recommended for small tile but there’s other options. Green skin, other isolation membranes, add subfloor with DMX and tng osb before tile and tapcon to the floor, etc

Don’t even touch the PEX pipe…. Just use this fitting . I use these all the time. They will screw onto your shut off and tee from there. Then you can get a 3/8 brass compression cap for your unused shut off on the cold