gfsemi If the EA App thinks you down own these packs, under Sims 4 > Manage > Manage add-ons, it's likely you're in the wrong account. The external drive has nothing to do with this; it's purely an account issue. Try signing into the EA App with any other email address you have.
If the App thinks you own the packs, under Manage add-ons, but they're not installed, or they show as installed but don't load in-game, that's a separate issue. For the latter, please see the accepted solution of this thread:
https://answers.ea.com/t5/Technical-Issues-Mac/Sims-4-packs-aren-t-loading-in-game/td-p/13765952