Can't hear it well. I don't think it's strut mounts or belt slippage, but I'm going to make sure we rule them out like good technicians.
If you turn the wheel with the key on, engine off, does the sound remain present? This will help isolate the issue to either the rack/pinion/pump/etc or suspension noise.
I think what's happening is an issue with inadequate pressure or something similar in the power steering system. Is the steering effort increased, as far as you can tell?
My suspicions are along the lines of of jolt's, that the rack or pump is failing or a hose is restricted. I'm afraid I don't have a suggestion for telling which is the weak link. The operation of the pump and rack are so closely linked that the failure of one might cause the other to appear failed.
I also think that if one has failed, the resulting strain on the other components might make it a moot point anyway. This is a common consequence for many vehicle systems where one component must take up slack of another. So please take that into consideration, as you may well end up needing to replace everything involved anyway. Even if the part that did not fail seems OK, it may have had a dramatically shortened service life later on down the road. Just make sure you set aside enough funds to replace everything else once you identify the culprit.
You could probably get used parts as replacements, but they may be sensitive to contamination or being drained and corroding while not being used; not sure.
PS: you have done a great job trying to diagnose this on your own and have shown great initiative. It makes me so happy to see someone approach a car problem with some logic after the nonsense I've seen on the BMW forums lately.
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