I was finally able to fix it. Even though I was signed into my Xbox account on my Xbox console, I discovered that I had been signed out of my Xbox account on the internet (on my computer) while I was searching for answers. Once I re-signed in on my computer, I was then able to link my account in the Sims, and when I re-started the game I just had to re-download the missing Maker Pack.
So I think the problem had to do with Microsoft and their weird account sign-ins. I don't know why it showed that I was still signed in on my console, but at least I got it to work in the end.