A number of factors are at play, mostly weight transfer as mentioned above. Under acceleration, the weight is transferred rearward, making the car lighter up front. When you lift off the throttle to shift, the acceleration force goes away, and the weight shifts from the rear to the front, giving the pitching sensation. The other element on the ST is that it is a FWD car, so the engine torque causes the motor and transmission to roll fore and aft under acceleration and de-acceleration. On a longitudinal mounted engine, like a RWD car, the motor torque causes rotation left and right and not fore/aft. When you are accelerating, the torque causes the engine to move one direction and then lifting off the accelerator moves it in the other. Due to the massive amount of weight of the drivetrain, you feel it in the chassis when it moves. Those factors cause the pitching motion.
How to fix it? Well, there are a couple of options. First is to limit the amount of motion of the motor between acceleration and de-acceleration by using a stiffer bushing in the lower motor mount/rmm/torque mount/roll restrictor (same part, just a number of ways of naming it). Next is stiffer springs and matched dampers which will limit the amount the chassis pitches on the suspension. Finally, a shorter throw shifter to reduce the amount of time between shifts. The less time between shifts means less time for the weight to transfer from one end to the other and then back again.