Same exact problem and symptoms last year….turned out to be the DSC module. Other likely contenders can be a wheel speed sensor failure or, as you pointed out, an alternator.

The primary ground under the hood is down by the ac compressor, on the right side of the motor. It’s below the secondary air pump, if you guys have that over there. I’d check that one first, and after that I’d pull the trunk apart as there a several back there.

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Current
Original owner 2002 E53 X5 4.4i to 4.6i swap
2025 G06 X5 50e
Former
1972 Audi Fox
1986 Saab 900S
1996 BMW Z3
1998 BMW E36 M3 Sedan
2004 BMW E46 M3
2006 Audi A3 Quatro
1993 Mopar 318 Jeep Grand Cherokee
2015 V6 Jeep Grand Cherokee