Watch the clutch while somebody presses the snowflake. Take a slomo video even better.

It can be tricky to see the inner part spin since the outer pulley off course always spinning.

Also: in software you should be able to read status of the clutch.

I suspect the clutch air gap is off and not grabbing or variable displacement compressor is stuck at zero displacement until you rev.

You need to figure out if the clutch is grabbing

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)