Will a 2022 Ford F-150 tow a 2027 Forest River Grey Wolf 28QBH?

No, it's over the limit

Over on payload.

• Tow rating: 295 lb to spare (7,905 lb camper, rating 8,200 lb)
• Payload: Over by 254 lb (1,659 to 1,896 lb used, payload up to 1,405 lb)
• Truck and trailer together: Not sure yet (14,915 lb, GCWR up to 14,650 lb)

Hitch setup

• Weight-distribution hitch (needed): Your camper is over 5,000 lb. Most truck makers require weight distribution here, and many receivers are rated far lower without it. It spreads the tongue weight to your front axle and the camper's axles, so the truck sits level and steers right.
• Sway control (strongly recommended): It stops the camper swinging side to side in crosswinds, when semis pass and on rough roads. At about 33 ft, your camper catches a lot of wind. Many weight-distribution hitches have it built in.
• Spring bars rated about 1,000 to 1,500 lb (size): Match the bars to your loaded tongue weight (949 to 1,186 lb, from an estimate of 12 to 15% of the camper's weight) plus anything heavy behind the truck's rear axle. Bars that are too stiff ride rough. Too light won't level the rig.
• Brake controller (needed): Your camper has electric brakes, and the controller in your cab runs them. Many newer trucks have one built in.
• Measure your tongue weight (tip): We're estimating 949 to 1,186 lb. A tongue weight scale or a hitch with a built-in gauge gives you the real number. Enter it in step 2.

Hitches make towing steadier, but none of them raise your tow rating or payload. The hitch itself counts against payload.