It seems the time has come, EA has begun the process of swapping from Origin to the EA app on Steam, which could cause a few issues for Linux and Steam Deck with Proton. Multiple titles on Steam got updates within the last day, with no patch notes or announcements from EA that I can see. The only difference seems to be introducing the EA App.
Checking my existing install of The Sims 4 on Steam Deck and it seems fine. It briefly showed a new EA App screen, then showed Origin and then went into the game.
An existing Titanfall 2 install on Fedora Linux (desktop) however refused to initially launch, it gave me the EA screen and with Proton 7.0-4, Proton 7.0-5 (RC) and Proton Experimental it just wouldn't launch. Removing the compatdata folder, where all the Wine / Proton prefix data is stored and reloading got it a bit further, to some sort of blank EA App screen after successfully installing it that got stuck. Killing all Wine processes and exiting Steam, then reloading Titanfall 2 and after a few blank EA App screens appeared and vanished — it works again.
With a fresh install of Titanfall 2 on Steam Deck with Proton 7, it had the issue again of a blank EA app screen that got stuck. Quitting and reloading, it once again showed the blank EA app screen. Forcing Proton Experimental on it, and then it actually worked.
Trying a new install of Star Wars Jedi: Fallen Order on Fedora Linux (desktop) with Proton 7, and a similar issue as the above although it didn't need a compatdata folder removal. EA App seemed to install, then I just got greeted by a blank EA App window. Seems it's actually a sign-in window, as I was able to highlight things on it by trying to drag things out of the window. Anyway, in this case simply quitting and reloading just seemed to fix it.
So it's a bit of a nuisance and acts differently between games, but it appears the EA app can still work with Proton but it might need a little extra work.
Note: the below can remove settings, possibly saves etc, do at your own risk.
If you find you also need to remove the compatdata folder for some EA games (for Steam Deck, be in Desktop Mode): find the Steam App ID (Right click a game -> properties -> updates) or grab the ID from the URL of the Steam store page for it. Then inside your steamapps folder you will find compatdata and inside a folder with the same ID. Where it is depends on what drive you have games installed on, the default is
Let me know in the comments how things are going for you on various EA games on Linux desktop / Steam Deck now.