For the heck of it, I would try another battery out of another vehicle just to see if its the battery.
I would also try disconnecting the battery for 30 minutes and then reconnecting to see if it helps the computers. German electronics can get very grumpy
Chris
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'22 M5CS, '06 Z4M, '01 X5 4.4i, '00 M5, '05 Acura RL, '12 X6 3.5, '01 740, 08 335xi, '17 540xi (yes they all are still with me)