You did not supply your year so I just guessed at one. E81 >2005/08 Looking at the power supply schematic you are correct. I did not dig much deeper then the schematic and not being familiar with bmw radios this is mostly just guessing but Your aftermarket is probably designed differently requiring a KAM (keep alive memory) supply at all times. and the power ...
factory reset your audio? or what?
could you please elaborate?
if the the audio docks you can try to search what kind audio brand you are using..
example : JVC
and the type example : TF67B
than you can look it up to google, check if there is a firmware update and how to update the firmware to open HDD.
I believe that the " ._ " files are being created by your Mac, possibly these files are confusing the head-unit of system.
Look into Why are dot underscore "._" files created, and how can I avoid them?, which seems to have more information on these files generation and getting rid-off them.
I think you probably need to take an approach of changing things, possibly changing everything, until functionality is restored:
Change the USB disk for another capacity, speed and brand. Perhaps even format it using the head unit if you can
Ensure the files are named correctly by your mac (plug the drive into another device like a smart TV or computer and ...