i'm experiencing everything that you're all describing above. 2016 440i, currently 42k miles.
after years of sitting on it (and then covid etc.), dropped it off at the dealer yesterday.
I took the technician out for a test drive, replicated the sound, which he acknowledged.
They've had the car today and couldn't find anything wrong with tensioner/pulley/belts (or something) etc. (that was his initial theory), called me today and said that BMW Germany have asked to place some mics around the engine, turbo and gearbox, they're going to record the noise and send it across to them to find out if its normal or not.
I'm not convinced the mics will pick it up if they're being placed directly next to components, maybe they'll also record from interior, not sure.
what i find strange is how it appears then dissappears, the moment you stop driving hard.
Once car is warmed up etc... i have to do maybe 2-3 WOT pulls from 10mph to 50, the noise will appear on maybe the 3rd run, and remain, as i repeat the pulls.
Then the moment i stop, cruise around for a bit, and try it again - i have to again do 2-3 pulls for the noise to reappear.
If it's transmission related, wouldn't the noise be present all the time?
i have a feeling BMW will just say 'yup its normal' and be done with it, who knows. The problem is the technician has to drive it for it to be actioned with BMW, so all of this is now dependent on him being able to do the above tests in a competent manner... he was sat next to me as i did it so hopefully he won't pussy the car around.
I'm not fussed either way, at least i've done my bit and flagged it - there isn't any moment during daily use where i actually do continuous pulls, so it's never an issue.
Guess i'll continue extending my comprehensive warranty indefinitely....