We don't carry more than 150 pounds of gear, so following some basic math, a dry weight of just over 3000 pounds plus 150 pounds equals about 3200, not 4000.
I have a -very- similar (but older) truck than you have - engine, gear ratio, the works. You should be good overall, but I think you forgot something...
That would be 150 of gear -plus- fresh water (assuming you don't add more as your gray and black tanks fill) -plus- propane (20-60lbs or more extra including tank weight, depending on configs, since they never count that), plus any/all additional tackle tossed in for weight/level/etc. Also, not 100% sure if the WDH counts, but if it does, that's 80-90lb or so more you'll have to account for.
(note that as long as you only do full-service campgrounds, you can possibly get away with having empty water/sewer tanks everywhere you go, but only if that's always the case and you can always get a full-service spot with a dump -right there- next to your parking spot. I intend to be way too much into boondocking for that ****, since I've always camped remote with previous RV trailers.)
I have a truck almost exactly like yours right down to the gear ratio, but it's old(er). My 2022 Forest River NoBo 19.2 weighs 3600lb empty, but once loaded, I fully expect to come fairly close to my truck's absolute limit of 800lbs more (240lb of it is just the water in a full fresh tank!)
Now for the good news - your body, frame, and (hopefully) your hitch will be -more- than capable to drag the (far more realistic) ~3600 lbs of stuff sitting in the trailer. Mine handled 3600lb of dragging it home through mountain roads like it wasn't even there most times (you'll still feel it on the inclines, though), even with no WDH. So, I think you'll do fine.