Good day,
I also have a 330i from 10/2019 and it is the same behavior.
So your car is normal. Works as designed.
It usually shifts into 8th gear at 67 km/h. Sometimes even at 64 km/h.
The restless behavior occurs up to 70 km/h.
But even in the lower gears it always shifts to around 900 revolutions per second.
Climbs on hills lead to significantly higher speeds. Then it doesn't shift below 1,000 revolutions. As soon as it goes level or only slightly uphill, it does it again.
It's actually usually 860 revolutions, a little under 900.
7th gear is engaged at 56 km/h.
6th gear at 44 km/h.
Everything's fine, you don't have to worry.
It is important: in cold temperatures pay attention to the Newton meter display and only accelerate at around 70nm, otherwise it will damage the engine. Especially when changing strokes to 900 revolutions, the load often goes up to 130 newton meters, which is very bad when the engine is cold. So give it less gas!
OR you give MORE gas and it will shift gears later!
Info: Sport mode leads to later gear changes, but these are also faster and not so great for the cold transmission. I wouldn't see it as a solution!
Info: The transmission control in the 330i with sports automatic transmission (has paddle shifters) is more aggressive than the control in the normally configured 330i.
Anyone who is not familiar with this behavior is A) very sporty and the transmission has learned to shift gears late, right
B) has paddle shifters, i.e. sport automatic transmission.