I had a similar handling issue when i got new tires , Bridgestones RE050s same as the OE ones i had earlier. The issue was narrowed down to tires as dealer replaced all 4s from another car to check which solved the problem.
And dealer got BMW to replace the front 2 as apparently there was some issue with the tires, maybe they were sitting at the factor for too long, or rubber had gone bad.
I would have thought that issue was due to rear tires but replacing the front ones solved it! It was a free replacement done by dealer as problem started immediately after i got a new set of 4
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