I’m no more educated on half ton specs than the next guy with internet access and a fairly friendly GM dealer but:
Check out any of Chevy’s towing guides, they will answer how to spec a pickup to get to certain towing capabilities.
To get into the 13,xxx’s with the diesel, you have to have 20” rims (gives you heavier springs for some reason) and a short bed with the NHT max tow package. You can spec it this way to this day. Search on any car sale website with the keyword “7300” to find ones for sale. They are out there. I made this account just to reply here and I can’t add links yet. Just excited to participate
Anyway, any time you find a current generation 1500 with 7,300# GVWR you have a NHT truck with 3.73 rear end regardless of 5.3, 6.2, or 3.0 diesel (though the gassers may have a 3.23??? Still a 9.75 ring gear though I am pretty sure).
I got the privilege to spec a new work pickup the beginning of 2022. I wanted an LTD as they had great deals going on at the time, but I missed the order window by like a week. I ended up with a 2022 facelift LM2 NHT truck and I will drive to the wheels off of it. I love it. Mine got built February of 2022 and I took delivery on April 7th. Almost had it for 2 years now, just rolled 82,000 miles.
Mine is a standard (6.5’) bed with 18” rims which puts the GCWR at 17,800, bumper pull trailer at 11,700, and gooseneck of 8,100. With a short bed you gain another 100# of capacity, and with 20” rims you gain GCWR and ~1,500# of trailer (but not gooseneck interestingly enough). I would have loved that capacity, but the packaging that the 20” rims came with didn’t fit my fancy, cost too much, and I didn’t like the availability of tires.
These engines are amazing if taken care of, LM2 or LZ0. Also it’s a new truck. Honestly you can pull more with any new half ton than you could with most one tons from 25 years ago (if obeying factory ratings). That being said, no matter how you spec it, you will run out of rear springs or rear axle capacity before trailer capacity. If you are really aware of balancing a trailer, pulling 13,000# every now and then is well in the capacity of these pickups. When you load tongue heavy, you get in trouble quickly.
I work in agriculture service and see plenty of mixed driving in all conditions. When I pull a trailer, it’s a 14,000# car trailer (5,000# empty, it's a tank and I wish it was lighter). Heaviest I’ve been is 19,000# combined and hauled about 200 miles one way at that weight in the summer at 85F through hills and on the highway at 70mph. No issues. When towing I see 14mpg and 25mpg empty. Lifetime average is 24.1mpg.
In summary: get a 3.0. Period. You will not go wrong. If you are savvy enough to find an NHT and know what you have, load it properly and let her eat! Otherwise, keep your trailer below 10k and your tongue weight legal, and you will have plenty of engine to pull. You will run out of frame, axle, and springs well before you run out of power, braking, or cooling capacity with any 3.0. If you don’t pay attention to how you load a trailer, buy a 3/4 ton.