My friend who's moving, has a '19 suburban with a 5.3, and he's been pulling a 12' enclosed trailer with it during the move. Many trips to Canyon Lake (near San Antonio/New Braunfels) from Alvin (south of Houston) loaded with models, toys, etc. This is the same trailer he hauled to Austin last month for the Roundup, and a couple weeks ago to the model show and contest. Those boxes are heavy; I've helped with loading, packing up and unloading the trailer several times! He says it hauls fine, and I don't know if he uses tow/haul function. His prior suburban had a 6.0 and he had the transmission replaced at least 3 times (so maybe not!). It hauled the same load and trailers....
I've ridden in it with and without the trailer, and I can tell the load does affect the performance. Not a lot, but it does. He needs my one ton LoL....