Would a tire rotation on a 2018 Ford F150 cause the TPMS to read higher?

I have a 2018 Ford F150 I purchased new. It has 11,500 miles on it. I had the tires rotated on it recently. Since then, I've noticed two things. It is pulling to the right and the tire pressure reading from each tire is 3 to 4 pounds higher by the TPMS reading than by my manual tire pressure gauge readings.

The manual for my truck says it does not need a TPMS reset if the tire pressure should be the same for all 4 tires (which is true in my case). It also says you can just drive it for 20 seconds to reset it (I've driven plenty). Is there anything about a tire rotation that should have caused this in each tire?

Sure, if your tires were unevenly worn out, it could.

Road have a natural hump in the middle so you naturally would pull to the right and so to does the car heading your way so you both head for the ditch instead of a head on crash.
. Nothing should have changed in a tire rotation… Because nothing was changed but the wheels… The rear moved to the front and the front to the rear and that is it. That does not affect wheel alignment. Don't believe TPMS because it is electrical and electrical goes wonky first. Read your owners manual and learn how to reset the TPMS properly.

My guess is that the shop that did the tire rotation added air to your tires and they actually are 3-4 lbs higher pressure, and the manual/handheld gauge you are using is inaccurate. Those manual gauges are notorious for being inaccurate.

As for pulling one way - check the tires for uneven wear. Not just uneven wear on one tire, but check to see if one tire is worn more than others. Do this with a tread depth gauge. My guess is that the right rear tire wore out a little faster than the others since its the primary drive tire (this is common on rear wheel drive and 4x4 vehicles). The rotation moved that tire to the front which is why its now causing the truck to pull one way just enough for you to notice.

Many times a tire rotation will give you vibration you didn't notice before. The rear tires that were moved to the front are likely worn out of balance. Get all 4 tires rebalanced.
Set your tire pressures to the proper PSI listed on the spec ticker which is under the drivers door latch.
If you think your manual tire gauge is faulty check it against another hand held tire gauge.
The car tire pressure sensors are accurate enough to compare to each other but I would trust a manual tire gauge when setting tire pressures.

No. I would guess they added air to your tires when they rotated them. Most manual tire pressure gauges are notoriously inaccurate, unless you buy a good quality one.

Reset it and see. Your TPMS senses the position on the vehicle of each particular sensor. Use a digital pressure gauge for an accurate psi reading.

Rotating tires shouldn't effect the TPMS at all. HOWEVER, you may have to reset the system to account for the sensors being on different corners of the car.

Sounds like you are getting more braking on that one wheel. I'd pump the tires up to the max pressure listed on the tire sidewall and just leave it there. The only tire issues in the past 30 + years were due to lower than ideal pressures in the tires causing premature failure due to increased internal tire wear. In other words, the car manufacturer undercut the tire manufacturers engineering to give you a "softer ride". Happened with Firestone and Michelin tires, exact same issue.