It's not out of the question that it may be time for rotors and pads.
The more you become familiar with this forum the more you'll read that guys upgraded their front rotors at 20,000 miles, more times than not, it seems.
I did my 2014 at 18,000 mi and were perfect up until I traded it in at 45,000 miles.

I'll soon find out if my 18's rotors are actually better this year than my previous 3 f150's that had the same thing... undersized front rotors.

The engine chugging could be as simple as unplugging the battery for 20 minutes to erase the previous owners driving habits. Also could need new spark plugs (doubtful). Guys that own a 15 will better informed than me.

Whatever it is, you'll figure it out. For the love of god block out the noise that an ecoboost would be immune to the same typical vehicle issues or quirks.

Congrats by the way..

 

Your skip-shift sounds normal to me. Same as my brand new '18 EB. As for the weird sensation when holding your foot lightly on the brake, if the Auto-Start feature is enabled, it stops the engine if you hold your foot firmly on the brake, but will not stop the engine with a light touch or if the truck is rolling slowly. Could it be that you're feeling the engine stop-start intermittently with varying foot pressure on the brake? Try replicating the same thing with the AS disabled on the dash button.

 

'15 5.0's don't have Auto Start/Stop. The downshifting is normal, and early shifts at light throttle are normal. Trans tuning is largely driven by CAFE concerns today. My 2018 (different trans and engine I know) sees rpm down around 1050 rpm after some light throttle upshifts. As to the nonbrake pulse when stopping, no idea.

 

Run it in Sport Mode if you want it to shift at higher RPM's. I doubt will notice it lug that way. Might even stop skipping 2nd when downshifting.

 

 

It's not a engine issue, you don't see it on the tach nor does it feel like the engine is missing at all. The pulsing is quick and rapid, not at all slowing down the vehicle which in my opinion is where warped rotors are obvious, especially slowing to a stop very slowly. Mine is with the truck barely moving, maybe taking 5 to 10 seconds for one rotation of the tire is when I feel the very quick pulsing. It may do this 50 times within one revolution of the tire. As soon as I release and let it roll under it's own power, issue is gone. You would think brakes or ABS but it seems way to fast acting to me for brakes. As for the trans reacting to your driving habits, I personally have never heard of this and I need to read up on this. I did try allowing the truck to run in sport mode and the shift patterns are considerably higher and I barely feel the issue. No clue if running in sport mode hurts anything long term??
It also downshifts properly in sport mode, 3rd to 2nd. I find it challenging to believe FORD has these set up to downshift from 3rd to 1st during normal driving. I hope others comment on their situation because if they all do this, I'm fine. Honestly, in the back of my mind, I have a slight transmission issue I'm dealing with...Maybe not. I will also call the local FORD dealer and find out if the factory power train warranty is still in place with my rebuilt titled truck. If any of these readers are associated with dealers, please give your 2 cents.

Thanks so far everyone...

 

 

Not sure on the 13th gen, but a KAM reset on a 12th gen would sometimes take of problems like the OP has. Funny how nowhere in many threads relating to the 13th gen is this even mentioned.
Keep Alive Memory, KAM. Disconnect your battery negative cable for 15-20 minutes. Reconnect, reset any crap on Sync/radio/clock it may have disrupted, then go for a ride. You should notice a difference, until the truck relearns your driving habits. Good luck.

 

I have a 2015 5.0 screw FX4 and have neither of the problems you mention. The chugging/purging you mentioned, to a novice like myself to all this electronic stuff, sounds like it might have something to do with the hill start assist.