there are some issues with battery cables and power distribution on this model. this needs to be checked.
also the alternator and battery (despite being new) need to be tested, and the vehicle tested for a parasitic battery draw
it is unlikely for an ECU to fail in this model, so I am not sure why they would be leaning that way, especially if they are not BMW specialists.
my best advice would be to move the car to a BMW specialist. If this shop does not specialize exclusively or near-exclusively on BMWs, then they are most likely not equipped to fully diagnose this car and are going to end up guessing further with your money.
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