Can an airplane's WXR see/show wake turbulence of another airplane's wingtips?

"WXR is very good at "seeing" air movement when there is enough moisture for the WXR to "see"

you miss the principle of weather radar, completely.
it§s not MOISTURE the radar senses. it's PRECIPITATION.

weather radar can be clear, yet there can be 100 percent humidity and inversion fog within radius of 100NM.

even the snow flakes are unsignificant when it comes to radar crossection.

so, the weather radar is of no use in detecting wake turbulence.
guess how they mapped the Venus surface.. hidden under clouds, for centuries. using the radiolocation.

No.

Weather radar is for weather, not turbulence (that's what the WX means). It relies on liquid or solid water in the air, so it cannot see movements of air that contains only water vapor. It doesn't have the resolution to detect the small patterns of wake turbulence or vortices, even if liquid or solid water is involved.

It's easy to avoid wake turbulence with some simple precautions, so even if radar could see it, it wouldn't be necessary.