I don’t have an auto so going out on a bit of a limb here:
The M44 engine has a notoriously rough idle. This is because to meet FE/Emissions numbers for certification BMW had to take out fuel and reduce the idle speed as low as they could get away with. My manual M44 had a ‘rough’ idle from new, when I looked into it I found out the dealer ‘fix’ was to just increase the base idle speed. I didn’t want this so have grown to appreciate the lumpiness at idle - at least I can feel that the engine is running!
With an auto, putting it in drive will increase the load at idle and make a poor situation worse.
Obviously you’d be better advised by someone with an auto but even then people’s perceptions and tolerances vary wildly. You may well get someone with the exact same issue as you telling you theirs is perfect.
If you can see variations in the idle speed on the tacho then that, to me, indicates something is wrong. Or if has become significantly worse recently. Otherwise it may just be what it is.
In any case, fixing your MAF issue can only help matters.