That UTP cable is just as much detuning your antenna by common mode current as
feeding the antenna by coax without balun would do.
Common mode current via the NanoVNA and the UTP cable to ground has just the
same detuning effect.
That detuning should be investigated;
I suppose it depends on match between nanoVNA and antenna.
For antennas typically using a balun to feed coax, then nanoVNA should have the same.
Perhaps running several turns of cat6 thru a ferrite core near the nanoVNA would mitigate.
Supposing that one has some other indication of antenna tune at the shack end of coax,
could useful experiments to minimize nanoVNA + USB-via-cat 6 impacts
be conducted with antennas conveniently lowered?
I have no feel/experimental results for Yagi proximity to earth...
Oristo