@luckypalmer Just out of curiosity, please open Macintosh HD (or whatever you've named your hard disk) > Library > Application Support > Origin > DownloadCache, and if there are any files present, let me know what they are and how large they are. (Or you could take a screenshot.) This is where Origin stores downloaded games before installing, and I'm wondering whether the game files are there and in what form, and also whether you could manually launch the installer instead. Probably not, but like I said, I'm curious.
If you don't see Macintosh HD listed in the left panel of a Finder window, click Finder in the upper left corner of your screen, select Preferences > Sidebar, and check the box next to hard disks.
If you can't install Sims 3 that way, please run the Origin reset tool, restart your computer, and try to download only the base game. You can deal with the packs later, but they won't install if the base game isn't present.
https://help.ea.com/en-us/help/origin/origin/how-to-reset-origin-on-mac/
Just to clarify by the way, the 64-bit version of Sims 3 does have a minimum requirement of High Sierra (OS X 10.13) or newer. Since you're saying the 32-bit version is incompatible with your Mac, it sounds like you're running Catalina (10.15), but just in case, please double-check what OS you're running. Click the Apple icon in the upper left corner of your screen and select About This Mac, and you'll see your OS listed along with the other specs of your Mac.
