It isnt shown well, but the axle from the hs motor will have 2 gears, 1 big, 1 small, and the opposite on the axle driving the wheel. So the servo will have a metal lock plate on it, connecting to 2 axles with universal joints on their ends, which would be used to change the gear ratio. Do you think this would work?? Sorry for the bad drawing, I’m not used to drawing with a touch pad.
I’m not sure what you are asking. Yes, a servo does work for shifting a 2-speed transmission. Yes, it is at least theoretically possible to build a holonomic drive with a 2-speed transmission. Yes, you can build a holonomic drive with a 2-speed transmission shifted by a servo. I think the more interesting question might be how to do this while leaving enough motors to operate your other mechanisms, as you might have to use two servos to shift all four wheels.
Holonomic X form as shown need one independent motor per wheel.
If you have a gear box per wheel that a servo can shift by moving a lever,
then you just need to work out the mechanism to have one servo shift all the levers at the same time.
If your drawing was intended to show that such a mechanism can be done
with a U-joint, I didn’t understand it, perhaps because of the low detail,
or merely my own limitations.