I too ran into this issue but I seem to have found a work around (for now) and at least get my controller to work but still has the xbox inputs (showing x,y,b etc but its better than it not working).
Ill just list the steps I did and hopefully it works for everybody else
1) Add Madden 20 as a non steam game on steam
2) Plug in your ps4 controller and turn on DS4 (idk about xinput i use ds4 personally)
3) Open big picture mode on steam and run madden from there
Your controller should work from there and you'll be able to play but like i mentioned it will be with xbox mappings
It sucks that we have to do this and EA really needs to fix this issue so we dont have to go nine miles just to use a ps4 controller with origin and madden