@lbuesch2 Since it's quick and simple to try, please force the game to launch in windowed mode. (I'm not all that confident it'll help, but it's easier than anything else.) Go into Documents > Electronic Arts > The Sims 3, open Options.ini, search for fullscreen , and set it to 0 (zero).
The initialization error is often related to broken or missing registry entries, which in a fresh install is usually caused by a system issue or an overly active antivirus. So if you haven't already, please clear the EA App's cache and repair the game with your antivirus temporarily disabled. As long as you don't do anything else at the same time, your computer should be safe.
https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/
If that doesn't help, uninstall Sims 3 and the EA App with Revo Uninstaller (the free version is fine), and restart your computer before reinstalling the App. Create a new folder into which you'll install Sims 3. The folder should be on the root level of the drive of your choice, for example C:\Games is fine, but not C:\Program Files\Games. Leave your antivirus disabled while reinstalling and for the first time you try to play.
You'll of course need an Alder Lake-related workaround, and repairing and reinstalling will both undo the effects of the patch. Rather than running the patch again, please use the Task Manager method covered here:
https://answers.ea.com/t5/Technical-Issues-PC/Sims-3-won-t-open-Alder-Lake-Intel-12th-gen-CPU/m-p/11720109#M251930
It's the most inconvenient but also the most reliable, so it's the easiest way to make sure the Alder Lake issue isn't the current problem.