First Transforce either HT or AT are both about as quiet of tire as you can get. Neither are open/agressive lug pattern.
Noise increases with the aggressiveness of the tire tread in general unless splitting hairs.
smooth ride is largely a function of air pressure and Id hope/assume you’re running not much over the recommended min pressure for the weight. Which with a dually and a little bumper pull trailer is, well, very low.
You can easily be running 35-40psi in your rear tires with that camper, unless you have a (literal) ton in the bed also.
None of this has anything to do with a particular brand or model of tire. Air pressure relates to load capacity the same across all brands/model of the same tire size.
you could drop down to 215s to get more squish in the rear but it’s of little consequence really. Just at your pressures to what you need to for load and comfort.
pick the brand/ model of tires based on your budget or preference. Noise or lack of will follow the tread style. Comfort will follow your tire pressure gauge.