TBH If possible launch games purchased through Steam (EXCEPT for EA games) with Steam.
If finding an EA game on Steam, sign out of Steam. Install EA App if not already done so, then purchase directly through your EA account/app.
I started doing this approx 3 years ago because sometimes I had problems, as explained here and elsewhere when linking.
Better to use 1 launcher for one game. I have no idea about EA Play as I don't use it.
The result: Since launching any game directly from EA App (rather than linked) not once has it failed. That's several hundred launches at least of about 12 games over 3 years.
It's worth a try if frequent link problems like I had. If no problem, no need.