I can't answer your question exactly, but I had kind of the opposite problem. So can confirm that the diff oil DOES make a huge difference.

Had a W126 with the same noise you describe. Tech looked at it and said both rear wheel bearings looked good, but the left side looked a "very little bit" more worn than the right. He didn't want to change them, saying it was rare for a W126 rear wheel bearing to die.

I made him change the left one. Noise still there.

Replaced the diff oil myself and the problem went away completely. I drove the car another 100,000km (60k miles) before I sold it and the noise had never come back.

So for sure it's the diff oil.

I would avoid the WM stuff. I put Mobil 1 in it (not sure what grade but I believe there was only one grade that MB approved)

Look up the MB list of approved oils, buy the Mobil 1 version, and change it.

Not too expensive as there isn't much oil in there at all.

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