I am having the same issue. I have followed all of the steps suggested so far (Deleting the file, clearing the cache, creating a new Sims 3 folder/file, and changing the password. I even tried to use Chrome, Firefox, and Edge to download it into the launcher and I am just constantly asked for my password.
[CM Edit: Split post, title update]
@tennismon Did you specifically clear Edge's Internet Explorer data? That's where the launcher stores its cached data and what needs to be cleared. Here's how:
If that doesn't help, please create a new admin Windows account on your computer. Make it local, as in, don't link it to your Microsoft account. You'll be able to open the EA App and the Sims 3 launcher without reinstalling anything, so please do that and see whether you can sign in, and whether you can download Store content without signing in.
