@Arishka145 That should be fine, both overall and for my next suggestion if this one doesn't work. First, please repair the game once more and see whether that helps, still using the clean folder I mentioned before. And try downloading the content using Firefox.
If that doesn't help, please create a new admin user account on your Mac. Don't connect it to your Apple ID (you should be able to skip that step). Open Origin in the new account and repair Sims 3, yet again, which will create a few files that tell Origin you own Sims 3 and that wouldn't exist in that new account. Try to download one Store item in the new account. After downloading but before installing the item, close the launcher and open it again. When you click Install, look for a second plumbob.
In the new account, Sims 3 will create a user folder directly in Documents > Electronic Arts. You could move this to the external drive with a symbolic link, but please don't do that yet—it would be best to see whether the Store content works with as few potential complicating factors as possible. An otherwise clean folder with one Store item won't occupy much space at all.