I am towing a Forest River 263BHXL with a 2020 Silverado, 5.3LV8, max towing of 9800 pounds, max payload of 1924.
Your GCWR is probably 16,800. (Mine is only 15,000.) I also believe you must have the max towing package to have that max tow rating, and the 3.42 differential.
Your payload may be slightly more than mine, but I suspect it is similar, since your truck probably has a few bells & whistles that subtract from the payload. The 27RK dry hitch weight is 270 pounds more than my trailer, at 955 pounds versus my dry hitch weight of 682 pounds.
I have never weighed my hitch weight, but I suspect it is pushing 800-850 pounds. If you add a similar 120-170 pounds to your dry weight, you are going to be at a hitch weight close to 1100 pounds. Not sure the max tow package allows for a tongue weight that high. Definitely will need a weight distributing hitch, at another 100 pounds. So, assuming roughly a 2000 pound payload, that leaves 800 pounds for all the occupants and cargo in the truck.
Others are also going to point out your trailer length is too long for your truck - as is mine. However, your trailer over 1 1/2 feet longer than mine.
My trailer is the most I would consider towing. Anything longer/heavier should really have a 3/4 or 1 ton truck.
FYI, I also notice that 27RK is almost a foot taller than my trailer as well, from a headwind and crosswind consideration.
2020 Chevy Silverado 1500
Forest River Wildwood XLite 263BHXL