To those PM's...
First, thank you for your comments, but I do NOT comment to Proverbs 26,4 folks...
Did NOT say NO, but provided info on HOW2 figure it out to the OP with information of mine and pointed out that the OP should look their glove box manual...
Also have a half ton with a 6K GVWR and have towed many things with it...including a Coleman PUP that was in the 3K range (never weighed it). Ditto my Odyssey. Daughter in S Calif had one and towed it with both vehicles and my K3500 Suburban
My 1980 half ton Silverado was a fake half ton (almost 3/4 ton ratings) of it's era (today's fake half ton will have a GVWR in the high 7K's to low 8K's), but is similar to the F150 the OP is considering or posted info on (in the lowest class of pickups and of that...the lowest of that class).
Of course the OP is looking a a current era half ton and should be way better than my 37 year old with +500K miles on it...but that 37 year old will tow circles around my 2000 Odyssey and know the difference from REAL experience...and have towed & survived towing a +14K untility trailer that tossed this Silverado all of the wind farm back in the mid 1980's

Back to my 2000 Odyssey glove box manual page on MTWR and again, say the OP's should be higher as theirs is newer. Note the decline in in aux cooler or not and the decline in MTWR with added passengers.

Bottom line is still the OP's risk management decision (gambling) and makes no matter that the Odyssey has tons of car handling attributes...add that any PUP will NOT have anything near that kind of handling...so why make that comparison for towing with it?
The F150 TRUCK will tow it better, IMHO