Just 3 days ago (on 26 October 2022) all of my EA games on Steam got updated with a small 1 MB update. Then I looked on the game directories and found that Origin installer has been replaced with EA App installer.
Also when I launch one of the installed EA games (I have Battlefield 1, Star Wars Battlefront II and Star Wars Jedi: Fallen Order) for first time after the small update Steam performed a small first launch process, but it skipped EA app installation because I already have Origin installed.
The next day (27 October 2022) I wanted to install EA app and try the Steam game support again. I downloaded the EA app installer from EA website. Then checked the version info and digital signature. The installer have a version of 12.29.0.5286 and a digital signature date of 26 October 2022 (the same day as my Steam EA games got that 1 MB update). I ran the installer and installed the EA app and now my Steam EA games properly show up on EA app. Even launching EA games on Steam now redirects to EA app instead of Origin. So, the Link2EA system is finally migrated to EA app.
Thanks for the update.