Look at your voltages, could be a weak battery or alternator. Also check your accessory belts and tensioner.

Applying a slight load to the power steering pump is what’s happening when you’re turning the steering wheel. I’d start looking in the engine compartment instead of the cabin.

Just pray it’s not a terrible obscure electronic issue.

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2006 e53 4.8is Imola / Cremebeige
2005 e53 3.0 Black / Truffle - AT, Sport, Premium, ZCW
2001 e39 M5 Black / Caramel - Extended Leather, Premium Audio