DO NOT UPDATE AND REINSTALL ORIGIN. I AM HAVING THE SAME PROBLEM AS YOU AND I UPDATED ORIGIN, ALLLLLL OF MY SIMS 4 GAMES ARE GONE!!!!!!!!!!!!!!!!
You need to upgrade to Sierra/High Sierra, or El Capitan if your Mac cannot go further than 10.11. Your issue is well documented, EA are aware and are working on a fix.
You can read about your issue here - https://answers.ea.com/t5/The-Sims-Mac/Empty-Game-Library-Server-Error/m-p/6938454#M13245
Upgrade to El Capitan - https://support.apple.com/en-gb/HT206886
Upgrade to Sierra - https://support.apple.com/en-gb/HT208202
Upgrade to High Sierra - https://support.apple.com/en-gb/macos/high-sierra
Locking this thread as we don't need multiple posts on the same issue, feel free to post in the main thread if you need further help (here's the link again - https://answers.ea.com/t5/The-Sims-Mac/Empty-Game-Library-Server-Error/m-p/6938454#M13245) 🙂
