FWIW, You can get the TPMS sensors used in the Model S, X, and 3 from RockAuto for $47 each (The very early MS came with a "Baolong" sensor that was phased out in early 2014). Still, just an informed guess... If you can actually talk to someone at a service center, you could ask if they all use the same sensor (please post if you find out...).
It is not the same sensor. The aftermarket BLE sensors supposedly don’t work either. Search is your friend