European repair shop vs. Audi dealership for 3rd party warranty repair?

I bought a 2020 Q7 a month ago and I'm noticing a rumbling sound when I'm turning slowly in parking lots, or doing semi tight turns.

I have a 6 month warranty through Avantaguard, which was included in the purchase of the car. From looking online it's likely the center differential that's the issue, and it will likely need a fluid change, but if that doesn't solve it, perhaps a new transfer case?

My question: in my situation, the warranty says that the transfer case and any internal components are covered. One of the service advisors at Audi said that the center differential is not incorporated into the transfer case, but I spoke to two different European repair shops locally here in Vancouver Canada, and they both said that the center differential is within the transfer case.

Do you think I should go with the audi dealership for this repair, or the trusted European repair shop which has five stars on Google? I'm just wondering if Audi will be more likely to tell me that it's normal, compared to an independent shop which will make every effort to fully resolve the issue, including possible replacement of the center differential. Also, Audi told me that the fluid for the center differential is on backorder, and not available in Canada , and they don't have any ETA, which can further complicate things because my warranty is only for 6 months. Thoughts? Thanks in advance.