I guess it's possible that the air pump might only be noisy if there is extra back pressure from the exhaust ?? Does it seem to change with that in mind ? (on coast or accel)

You should be able to hear the air pump running on a cold start and then maybe listen for when it quits before driving away so you get an idea of what it sounds like.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)