I recently played the same game, trying to determine if my 4Runner would be capable...and bouncing back and forth b/t the X17 & X19. And, while I haven't towed it yet, I did purchase the X19H and will share my process and thougths...and some numbers that hopefully are some help.
First, I used the spreadsheet found here to project all my weights
Thoughts on Towing
I also leaned on my father's 30 years of travel trailer towing experience and knowledge to help put together a list of items and their weights (from his personal list, he weighed every item that goes in his trailer before towing it). He also reviewed my total numbers and ratings, etc.
Looking quickly, I couldn't find a tongue weight rating for the Traverse. My 4Runner is rated for 500 lbs tongue weight, so I know I'll have to carefully load the trailer to stay under my tongue rating but near that rating as to keep the % of tongue weight in the 10%+ range. I plan to purchase a tongue scale and use it often.
As also noted, you'll have to keep an eye on all your specific vehicles ratings (GVWR, GCVW, Gross Axle Weight, etc). You may also want to check and see if the Traverse allows the use of a weight distribution hitch to help equalize the weight. Looking through the Traverse's owners manual in general to understand all the ratings and limitations would be beneficial (and likely confusing).
My 2021 X19H has a dry weight (as shipped with options) on the sticker of 4016 lbs sitting at the dealership. I've figured the following based 2 adults and 2 children:
422 lbs of gear in trailer (Food, tools, spare fluids, chairs, grill, coffee maker, pots/pans, clothes, way controls, etc)....you can split this b/t your trailer and Traverse but keeping an eye on the different ratings. I'm not carrying any bikes or anything like that b/c I can't handle that additional weight.
14 gallons on board (4 in blackwater, 4 in freshwater, 6 in water heater)=117lbs.
45 lbs for battery and 40lbs for propane (and I've planted in my head that removal of one of the tanks is an option if needed to reduce weight).
I have another 135 lbs of stuff in the truck, plus hitch weight and people.
My total projected trailer weight comes in at 4,640 and my plan is to practice loading it to get my tongue weight close to my max 500 lbs, but I know I'll have to keep an eye on this everytiime I travel as you'll burn off propane, maybe pick up something while traveling and need to figure out where it gets stored, etc and need to adjust. At least until you get to a comfort level of understanding the changes.
My predicted GCVW is 10,070 lbs. For my 4Runner that is 89% of it's rating. Projecting similar for you, this is pretty tight at 98% of your stated 10,250 GCVW rating of the Traverse.
To be honest, I'm maxed as far as I want to be (maybe a touch farther) on the 4Runner and I've told my wife this years travel will be the 3 L's:
Light Loading
Local Travel
Learning
Not sure where you plan on traveling or what the terrain is where you are at, but we know with this setup we won't be traveling cross country or into the mountains.
We also have a back up plan that if we determine that towing the trailer with the 4Runner just isn't working out that I'll be trading it in on a used 1/2 ton, 4 door pickup. And, with children growing and wanting to travel further I predict this will happen in the next 2 years.
Hope this info helps.....good luck in your decision!