@sapphiretiger Yes, that's what I meant. Steam wouldn't be able to download your EA-owned packs anyway; there's no way to make them appear in your Steam library. Since the EA App isn't cooperating, please uninstall it with Revo Uninstaller (the free version is fine) and reinstall.
If that doesn't help, uninstall the App and also Sims 4, both with Revo. Don't uninstall Steam if you have any other Steam games installed: removing Steam will also remove those games. If Sims 4 is your only Steam game, you can uninstall it as well, although it's usually not necessary.
If you have any saves or other user data you want to keep, go into Documents > Electronic Arts and rename the Sims 4 folder inside to something that doesn't include "Sims 4." This is so Revo doesn't flag and remove it.
Reinstall the EA App (and Steam if applicable), then create a new Steam library, as described here:
https://help.steampowered.com/en/faqs/view/4BD4-4528-6B2E-8327#default
The library should be in a new folder you create for just this purpose, and it should also be on the root level of the drive of your choice. For example, C:\Steam Games is fine, but not C:\Program Files\Steam Games. Call it whatever you want, just not "The Sims 4." When you install Sims 4, make sure it installs to that new folder. Then try again to download your EA-owned packs from the EA App.