Stopping a standing desks from rocking
If I see correctly, that your table legs are attached directly to the top with no apron at the top. That there is no rack bracing of any sort, short of the 1 1/2" by 3 1/2" faces and sides screwed together. The apron, when the legs are attached to it properly act as rack bracing to a great degree. Most table aprons are anywhere from 4 to 6" tall, although there is no hard and fast rule how tall it should be.

With a table that tall an 8" apron, properly attached would reduce wobble tremendously.

Moving it off the carpet would be a help too, since there is a 2X flat to the floor which does not allow the carpet to compress enough to give a solid setting. You could raise the bottom stretchers so the legs actually go to the floor, instead of on a 2X flat...