@UncannnyAnnie Alright, let's start from the beginning and do everything together. First, run the Origin reset tool:
https://help.ea.com/en-us/help/origin/origin/how-to-reset-origin-on-mac/
You need to expand the spoiler to see it; the reset tool is NOT the diagnostic tool on the same page. Once you've reset Origin, open it again, and if it doesn't do so on its own, repair Sims 3: open your game library, right-click the game icon, and select Repair.
Don't try to open the game yet. Instead, go into Documents > Electronic Arts and move the Sims 3 folder to the desktop. If it copies instead of moving, rename it to whatever you want. This will remove your saves and other content, but it won't delete the files—they'll be intact but unusable in the folder you moved or renamed. That can be addressed later.
Open the launcher to spawn a clean folder. Download one item from the Store, something simple like a hair or outfit, and try to install it. If nothing happens when you click Install, close the launcher and Origin and reopen them, then try to install that same item. Let me know what happens, and we'll go from there.