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Yeah, a +/- 1 cm oscillating steering wheel is quite far from normal! If you had no issues with the PSS then it definitely points to the PS4S being the cause/problem.
One thing you could try is have the tires dismounted, rotated 180 deg and then remounted or even remounted on the wheel on the opposite side of the car. Tire being out of round and/or a bent rim will cause a vibration even if they’re balanced properly. If you had a second set of wheels you could quickly find out if the wheels/tires are the problem or if it’s from something else on the car. Definitely take your car to a non-BMW shop because the ones you’ve been going to clearly don’t care about addressing your issue.
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