Welcome to the forum!
What you have a photo of is the AFM (Air Flow Meter) for the intake, not of a supercharger, at least in the pics.
Search for posts from 1996 328i as he is having issues, perhaps not as severe as what you describe, perhaps that will help you figure it out.
Sean, wasn't being mean. he prolly thought you were joking. I wondered the same initially as well. We'll help you troubleshoot.
Again, welcome to the forum!