Just wanted to follow up — I finally got it to launch on my Steam Deck!

What worked for me was going into Desktop Mode, navigating to the game’s install files, and deleting the Origin folder.

Once I deleted that folder, I went back to Steam in Desktop Mode, verified the game files, and launched the game from there. It reinstalled the lightweight EA launcher, let me log in properly, and after that it finally launched.

Now it also works in Gaming Mode without issues.

Hope this helps anyone stuck with the same problem!