@lima13bean No. The Sims 4 is the game. Origin is not a game. Please recheck the settings.
I think the best thing would be to start again with a clean installation of the game and Origin:
1. uninstall the game in Origin by right clicking on it in your game library and selecting uninstall. If the game is still showing on your external drive, trash the Sims 4 app and the Sims 4 Packs folder, empty the trash and disconnect the drive, in that order.
2. manually uninstall Origin following these instructions -
https://bluebellflora.com/how-to-uninstall-origin-on-a-mac/3. Empty the bin and restart your Mac
4. download Origin from
https://www.ea.com/origin-for-mac5. install Origin
6. plug your external drive back into your Mac
7. launch Origin and change the game library location to the external drive
8. install the game
Once you have done all that, and your game is downloaded and installed, let me know.