OP, you need to know if you have hydraulic or mechanical tensioner. #13 shows mechanical tensioner with pulley...but that's no longer a bmw part...it's shifted to all hydraulic now.
I just replaced my pulley...and although many are mechanical tensioners and take the 89133 pulley, some are hydraulic. You need to look and know what you have...or just order both and return the one you don't need.
See threads with 'pulleys' in the title...you'll learn all you need to know.
Of course, do the belts...and of course, do all three pulleys...since when one is gone, the others are close behind.
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A recent set--NSFW audio: https://youtu.be/_dcxcZfD6dg
Mangofy your E46!