The issue still persists.
I verified the game on steam, restarted the client.
Made sure the EA client wasn't running.
I press play on Steam and follow the steps till I get the same message "Something went wrong, head over to steam star over."
I even tried this: Uninstalled the client downloaded from the website,
then reinstalled it through Steam which downloads the EA App when I pressed Play.
Followed all the same steps and yet again I am stuck at "Something went wrong".
I also tried linking some other account, like my google account and it perfectly got linked with no issues at all.
Please let me know if there is update on the solution for this account linking between Steam and EA.