I have a 2017 MINI Clubman ALL4 which is the same drivetrain.
It appears to me that Hypoid G3 is the proper fluid. For that it’s just a easy drain and fill per the TIS. Actually not a drain, you have to suck it out the fill hole. I used my oil extractor with a smaller curved plastic hose on the end to dip it into the bottom of the differential.
RealOEM Shows Hypoid G3
https://www.realoem.com/bmw/enUS/sho...08#33108740374
New TIS is a bit less clear, as you mention. G1 vs. G3
https://www.newtis.info/tisv2/a/en/f...-drive/1EFiDSn
Genuine G3 is about $50 per HALF LITER. Yikes. I recently swapped mine out with MOPAR Synthetic Axle Lubricant which is the same 70w-80 GL-5 spec as the Genuine BMW G3. MOPAR part 68227765-AB. It’s about $25/quart. Although, I probably only sucked out 1/2 liter, so maybe one 500ml bottle will do?
Then there’s a separate fluid reservoir for the AWD clutch system within the rear axle unit. That’s BMW “HOC” fluid. “Hang on Clutch”. Looks like that’s the one that needs the dealer computer to both bleed and calibrate it. A bit more mythical on the Internet. Not much consumer-level info on the AWD system used in the newer FWD based BMW AWD vehicles yet.
I have a Foxwell NT530 computer/scanner and unfortunately it doesn’t have this function.
I also swapped my transfer case fluid (PTO box). That’s just plain-old synthetic 75w-90 GL-5 synthetic from what I can tell. I used AMSOIL Severe Gear Synthetic 75w-90 GL-5