erweg82zk66s The issue is that Steam will never recognize DLC you've bought through the EA App. You can use both together, at least in theory—the EA App could install the packs you own there into the Steam version of the game, and everything would load together. In practice though, this appears not to work in Steam OS at least some of the time.
As a practical matter, is there a reason you want to launch the game through Steam other than simple convenience? I ask because it might not be possible to work around the Steam OS limitation at this time, or if it is, it might take more work than it's worth. You can of course try installing only your packs through the EA App, after you've downloaded the base game through Steam; just don't count on it working.