Sims 4 on Steam Deck

@Lycostia  Are your packs loading in-game?  That message you see along the bottom is standard, or at least it used to be; it doesn't mean that the game or one of the launchers thinks you don't own Sims 4.

If your packs aren't loading, did you ever install another version of Sims 4?  There's currently an issue where the EA App dumps pack folders into the wrong Sims 4 folder, for example it might install the packs into the CAS Demo folder or a leftover folder from an older install of the game.  I don't know what the search function is like on a Steam Deck, but if you can search the entire file system for EP12 (High School Years) or another missing pack, you'll be able to see whether the folder is present and where it landed.

There should actually be three folders, and sometimes some files, for each installed pack.  The one inside a Delta folder is for patch data and isn't relevant here; the one inside Installer is also extraneous.  You're looking for a folder directly inside "The Sims 4" or something named similarly enough that the App might have gotten confused.  And of course the App is doing the installing of your packs since that's where you bought them.

If none of this helps, I'd suggest doing a clean wipe of Sims 4 and reinstalling only through the EA App.  You'll need to run it anyway, albeit in the background, while playing Sims 4 through Steam, and dealing with two game launchers is always more complicated than just the one.