EA app acts like there are no installed games

StudyInAlizarin​  The EA App doesn't have a "find game" function, formally or not.  It's completely normal that the App wouldn't see your already-installed games.  The usual workaround is to "download" games to their current location—the App often simply verifies the already-present files and finishes the installation.

Are you worried about Sims 3 or Sims 2?  I ask because there was never a 25th-anniversary update for Sims 3; the anniversary bundle only included 1 and 2.  For Sims 2, the Ultimate Collection from a decade ago and the newer version from 2025 are separate, meaning you could still install the UC in its previous form if you ever owned it in the EA App or Origin.

If you're referring to the January 25 update of Sims 3, that was only to fix the Alder Lake issue.  All mods that worked before the patch still worked afterwards, although core mods did start throwing an error due to the new internal build version.  Some, like ErrorTrap, were promptly updated, so you could download new copies to get around the issue.  For those that were not, I believe it's possible to edit the mods yourself to change the build number to match.

In case you're not aware, "core mod" means something very specific and uncommon in reference to Sims 3.  There are only a handful of core mods, with the vast majority being script or tuning mods instead.