I have a 2017 Silverado 1500. It is 5.3 8spd tranny 3.42 rear end. It has the max payload option so payload is 1950lb.
Our trailer is 31 overall and weighs 6500 lb loaded for travelling
The truck pulls the trailer very well. Long 6% grades are no problem - I can accelerate. The 8 speed is a definite improvement over the 6 spd which was way better than the 4 spd.
We find the interior very comfortable and quiet on long drives. And yes cruise,stereo and phone controls are on the steering wheel. The truck has integrated brake controller which works perfectly.
This winter we have towed about 8000 miles so we do have some experience with this combination.