My F-150 would almost be enough truck for your needs, provided you didn't carry more "stuff in the truck bed" and in the cab that I do.

Mine is 2019 F-150 Lariat 501A SuperCab with 6.5' bed, 3.5L EcoBoost engine, and max tow pkg. GVWR = 6,900 (max payload = 1,904). GCWR = about 11,000 with tow rating about 6,000,. To reach a tow rating of 7,000, you'd need to back off to XLT trim and omit my tailgate step and running boards.

Max tow pkg requires 3.5L EcoBoost engine, but you want that for towing anyway. It also includes the 36-gallon gas tank, and integrated trailer brake controller. However, it does NOT include the tow mirrors, so be sure to order those on your new F-150.

CAT scale ticket last week when towing my cargo trailer full of furniture for granddaughter, with Reese Strait-Line WD hitch
Front axle = 3060
Rear axle = 3120
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GVW = 6180 compared to GVWR of 6,900 = no problem with payload with wife and two dogs in the cab, tools and stuff in the bed covered with hard folding tonneau cover.
Trailer axles = 3,420 plus 500 tongue weight (TW) = about 4,000 trailer weight
Gross weight = 9,600 (GCWR 11,000)

Now, increase trailer weight to 7k and what happens?
TW goes up 400 pounds to 900. So GVW goes up 400 pounds to 6,580. Still no problem with payload capacity.
Gross weight goes up 3,000 pounds to 12,600. Oops! Overloaded over the rated pulling capacity of your drivetrain. So to stay within specs, we have to get rid of some weight. First is to replace the Lariat 501A trim with XLT 501a trim. Then omit the tailgate step and cab steps and that should get down back to the 11,000 gross weight.
Then to be sure you will have enough truck to never be overloaded with a 7k trailer, add the heavy duty payload package (HDPP) to the specs of your F-150. That will increase the tow rating to over 7,000 pounds as well as increase the payload capacity to give you more wiggle room for hauling heavy stuff in the bed.

But HDPP is limited to "long bed" models and with the fanciest trim being XLT 401A. On a SuperCab, the long bed is 8', not 6.5'. And you probably won't find any F-150s with HDPP in stock, so you have to plan ahead and order the special truck.. So most customers skip the HDPP F-150 and go to the F-250 with gas engine. You can get any trim and bed you want, and most big dealers will have "your" F-250 in stock ready to deliver to you. F-250 King Ranch SuperCab with 6.5' bed? No problem.

 

Regarding getting more truck than you need, the main focus of the towing packages is convenience and heat management. An HDPP equipped truck might be more than you need, but except for that, you're just trading payload for trim levels and body styles.

So the GVWR of your trailer is 7000lbs. Plan to use all of that even if you don't now, because life changes. Properly weighted, you'll have 900lbs of trailer on the ball, plus another 100lbs because you're going to need to use a weight distribution hitch. That's 1000lb of payload on the truck.

Add up what's going to be in the truck... you're weight, the SO's, any cats or dogs, luggage, bed liner, bed cover, high-lift mounted to a bedside rack... whatever. Add that to the 1000lb, you've got the minimum payload you're gonna need.

If you trade the trailer for a smaller one in the near future... you're not going to regret having the truck that can haul the trailer you have now. The truck you select won't be harder to drive or ride harsher than one with a lower tow rating. The factors that set these trucks apart are length, and running E-rated tires Vs p-metric.

 

My TT loaded is 7k I have a STX supercrew 4x4 with max tow. The weights on the trailer are crazy