Assuming yo have already performed a master reset and removed the car from the phone to later repair the both of them, if only the APIM was changed I would assume the HUB has not been replaced…
If so, try this as a reference guide → 2016 Mustang Sync3 1.0 updated to 3.0 and no Apple Carplay! - #10 by SaNdMaN
Once you are on 2.2.xxxx, try if CP works.
I’ve asked if you had an Android device to test this with since Android is more forgiving (or less picky) than iOS…