I am having the same issue. I purchased a custom bundle in the EA App. I bought Eco Lifestyle, Jungle Adventure, and Fitness Stuff. EA App does not show that I purchased these, however, I have a receipt that shows "Fulfilled" in the EA Customer Portal. When I launch Sims 4 it shows that I own the packs and tells me to download them. I exit the game, but the EA App still does not have the option to download.
I cleared the cache in the EA App, issue persists.
I also tried downloading the free My First Pet Stuff add-on, but the download won't start. It says to try again in a few minutes. I tried again, same error.
EDIT: During the uninstall process for the EA App, I selected the Repair option. I restarted my computer when prompted. When I launched the EA App, my purchased content was ready for download, including the free add-on. I hope that helps!