Didn't know the condition of the pedal wiring - but when the throttle pedal is "bad" - and even the original one does the same thing - I have had bad wires - those female connector sockets that mate the male body pins - go bad.
Have you tried to see if back probing the connector to the throttle pedal - there is a ground wire in that harness that connects to a bolt in the front firewall by that kickpanel trim - it's buried in there.
I have had instances where I have had to locate another bolt or make a bolt a stud (piano wire and pull thru a knockout) along with a kepp nut or serrated one - just to bite the ground metal and mount new ground there.
Not the funnest job.
This comes up when OEM connector and the new part that replaces the old part, the pins are off just enough to prevent the wiping and pinch action the female side does to grip the pin, The Socket side just lays loose and doesn't make proper contact. The original pins are oversized to the newer pins so the Female side developed a memory of the oversized fit the previous one made..
It's why you sometimes see some sensors - with the label - "Per OEM specifications" as a disclaimer to performance and warranty issues.
Else the pedal - being what it is, and if swapping the original - still does the same thing - there are only two options and Occam's razor is starting to show.
You have a pedal in your hand that got upgraded - or the OEM one was swapped and you got a bum one - the only way to know that is to double check the VIN engine code and the recommended pedal number to use...
The wiring from the Pedal is not making the trip back to the Dashboard and or PCM to tell it to move.- broken wire or poor ground - can't find "center" because as you already know - the pots use the source and ground potential difference to send a variable voltage signal to the PCM, and also the Dashboard.
... Third condition ...
You're working on getting a new sender sensor (that one under the intake - I believe) - is low pressure - the High pressure one is back at that can and looks for that diaphragm to strike it telling the system it has enough fuel pressure to make the GDI work.
But as part of it's troubleshooting effort, every time to "start" the vehicle - the APP (Pedal Position Sensor) is "zeroed" out by the system trying to find IDLE position reference - part of the learning process - the engine remembers and patterns afterwards looking at other sensors to make the start engine and run more smoothly and stay within emissions - easier as the engine learns.
So if poor ground - it can see it's hooked up - but the voltage is out of range so it puts itself in limp mode.
The big clue here is you can't make the throttle plate move with the pedal position - so that is a PCM to DASHBOARD and Throttle to APP communication problem.
Why? Because in several lines of the Focus model and even Fusion and Contour - they used Hall effect and carbon wiper in ways that were not interchangeable - but the connectors fit - so the wiring didn't work - but the pedal worked in other vehicles of the SAME line - just not is specific ones that used dual wiper pots, or hall-effect and wiper - because the PCM needed variable - and the Dashboard only needed Hall positioning (low resolution) and vice a-versa.
It's not too far out of the ballpark to know if - when you parked the car and it sat - and nothing else happened, then the "critters" and "Oxides of March" are marching into this scenario...
Now to bring up the "limp in" mode, that is possible - but you'd see that notification right away and the condition usually clears once the battery pull and reseat is completed to reset the flag on that.
But I've been able to clear the condition by reseating the throttle body connector and even the APP connector - and was able to start and drive off without having to reset and relearn - so I know the PCM checks for conditions on an ongoing basis.
This is certainly an interesting one..