@Theta-3119 and @SirForteske As you can see, EA is aware of the issue. Hopefully it will be resolved soon, and I'll update this thread if I hear anything (and if one of the CMs doesn't beat me to it).
@Theta-3119 In theory, you could call EA customer support and ask that the world be added to your account. But this wouldn't help you—worlds still need to be downloaded directly from the store. So as long as you can't login, you won't be able to install the world itself.
In the absence of a solution to the error 502, the only workaround I can think of is downloading your store content onto another computer. You'd need to install the TS3 base game first (you can skip the packs), and then open the launcher to spawn a game folder. Once you downloaded the store content, you could transfer the Sims3Packs in Downloads (inside your new game folder in Documents) to the computer where you currently play.
Two caveats: the new install would have to be the same type (Origin/Steam/disc) as your existing one, and you should use your own account to install on another computer, i.e. no borrowing a friend's existing install to download. The store content is encrypted to prevent sharing, and that also usually prevents different types of installs from using the same store downloads, although of course you can always redownload from your purchase history for free.
However, @SirForteske you may be able to go the EA Help route. Since Sims Medieval is downloaded from Origin, if you can get a support rep to add the code, you can bypass the store entirely.
https://help.ea.com/en/contact-us/