first, if it does not have a sway bar at all, or maybe it does have a factory sway bar, I would get a BigWig HD sway bar.
I don't know what the ford spring pack looks like, but I am betting IF it has upper overloads, you have the air bags inflated to high and the upper overload is not hitting the spring perch that stick out from the frame.
also if you have 1 air input, as you sway the air transfers from one side airbag to the other which does not help.
One way to fix this is to (lower air bag pressure) and to replace the rubber bumpers on those spring perches with something wider (like a hockey puck), or torklift upper stableloads.
But the problem with this is it can stiffen up the ride even empty if the new stableloads are hitting the upper helper springs.
on my 2006 3500 ram SRW I was running Energy Suspension rubber blocks to replace the metal blocks for my helpersprings. this stopped the "bang" (both noise and shock vibration you felt in your back) from the suspension every time you hit a bump loaded and the overloads banged into the spring perch. Plus they were rubber with holes so they had some give under load.
I have also tried the Torklift lower stableloads on a 2018 Ram 3500 dually. I loved them. they added around 1" of additional lift (back to level) with the 990 loaded. They come in Stainless, and you can disable them when running empty.
I tried Rancho adjustable 9000 on the rear and rancho 5000's on the front of a brand new 2015 Ram 3500 dually 4x4 (after working on phone with Rancho). this was a mess. I could repeatably hit a bump in a road and the back would start with oscillation up and down (with camper on) and would not stop until you slowed down to around 35. We replaced the 9000's but it still did it. I ended up returning them all under the "try them out" warranty rancho offered and put the brand new Ram shocks back on.
I had a sway problem with a Mercedes motorhome. This is a perfect example of a vehicle that is running at its max weight! First keep in mind a MH is always loaded, you can't take the body off like you can unload a truck camper.
It already had the BigWig Sway bar. I ran timbren blocks both front and rear which helped with the sway some.
Than I put Fox 2.0 shocks on the motorhome that were revalved for this application by agile offroad: WOW what a difference. it solved my problems!
but I can picture how rough the fox shocks might be on a truck if you unloaded the camper and drove around empty.
2022 Ford F150
Sold: 2016 Arctic Fox 990, 2018 Ram 3500, 2011 Open Range
Sold Forest River Forester 2401R Mercedes Benz. when campsites went from $90 to $190 per night.