@LoreGalore When you cleaned your computer's registry, did you by any chance also delete any registry entries related to the Sims 3 base game? If so, that may be why the EA App tried to download the game a second time. It's normally supposed to recognize the games Origin has already installed, but without the registry entries, and with the game likely not being in the EA App's defaul install location (you can see it's EA Games rather than Origin Games), the App may not have found it.
I'm also curious whether the game launches at all at this point.
Anyway, at this point, I'd usually suggest uninstalling the entire game and reinstalling to a different folder than the one it's currently in, preferably a new folder you create yourself (e.g. C:\Games). But if this is one lingering symptom of the partly-resolved EA-side download issues, you may not be able to reinstall the game at all, at least not until EA fixes this problem completely. I don't know when that will be.
Do you have access to a different computer where you could test? It would be useful to confirm whether the issue was particular to your system.