Will a 2027 Ford F-150 tow a 2027 Jayco Eagle 294CKBS?

No, it's over the limit

Over on payload.

• Tow rating: 700 lb to spare (11,700 lb camper, rating 12,400 lb)
• Payload: Over by 69 lb (2,114 to 2,465 lb used, payload up to 2,045 lb)
• Truck and trailer together: Not sure yet (18,260 lb, GCWR up to 18,400 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 35 ft, your camper catches a lot of wind. Many weight-distribution hitches have it built in.
• Spring bars rated about 1,500 to 2,100 lb (size): Match the bars to your loaded tongue weight (1,404 to 1,755 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 1,404 to 1,755 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.