Rev limiters on all modern engines are set at rev limits that the engine can run at safely (water and oil temp monitored) so you cannot blow up them up.
The Sport auto in Sport+ mode (manual operation via paddles or stick) will allow you to rev to the limit and hold it there in each gear but try to push past it and it will either move up a gear if one is available (Auto) or the engine management system will cut the power back (auto or manual) (I prefer that it changed up than cut power).
In low revs it will try to pull in the selected gear first if the torque is available or shift down if not (auto).
A manual will allow you to use the full rev range, however the engine management system will still cut power if the rev limit is exceeeded.
This is in the engine's protection system.
I cannot comment on how the auto performs in the 116i using a standard auto.
The rev range and torque of the 125i with Sport auto is very usable and the paddles are very predicable and responsive.
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