Add-ons are visible in EA app but not in Steam

jss26x​  It's normal that Steam doesn't display the packs you own in the EA App.  The way this is supposed to work is, you install the game from Steam, you download only your packs (but not another copy of the base game) from the EA App, and everything works together.

How are you trying to download the add-ons through the EA App?  Going through Sims 4 > Manage > Manage add-ons should work.  But if it doesn't, try clicking the Add-ons button above the Sims 4 base game tile and finding your DLC there.