There will be a little more manifold vacuum available to the brake booster when selected to Park, so that might be the reason why the pedal feels easier to push.
Most often the line from the manifold with its check-valve are exclusively used for the brake booster.
I would test the brake booster to see if it holds vacuum - it should hold vacuum for days if there no leaks - also check the vacuum hose and its check-valve.
Could you post a link to the specific seller/item.
How long did it take to deliver?
SE10001HPR Tire Pressure Sensors TPMS 315Mhz FOR BUICK CADILLAC CHEVROLET FORD GMC JEEP MAZDA MERCURY SAAB|Tire Pressure Monitor Systems| - AliExpress
Why create two threads on the same topic? - now merged.
The videos don't work.
Who's doing the install of these fuel pumps - might want to hire a competent mechanic.
There's one problem with that set - its missing the one that's needed for the brake calipers.
I recommend a 1/2" drive for this application.
4mm, 5mm, 6mm, 7mm, 8mm, 10mm
To me it sounds like that dealer lacks the skills to properly diagnose the issue - if possible find another dealer or make a deal with that one that if his parts replacement doesn't resolve the issue, NO PAY.
Please add your model, 2012 MKX, and location to your profile signature - https://www.fordedgeforum.com/settings/signature/
If you're wanting to scan for codes yourself you'll need to use a good OBDII adapter and FORScanLite.
Not sure why the dealership didn't retrieve any codes.
How difficult would this be for me to check if I need this or not?
The PDF @Haz attached shows it under one hour labor for the repair.
My dealership has in the past given me the recall parts for me to DIY and registered the recall as complete, which I might do for this.