If anyone here has this issue, Lazy Duchess (who released the Smooth Patch last year) has created a patch to fix the issue. Details are here:
https://answers.ea.com/t5/Technical-Issues-PC/Sims-3-won-t-open-Alder-Lake-Intel-12th-gen-CPU/m-p/11524785#M250970
In case anyone's wondering, you can extract the .zip wherever you want, then launch the patch and point it at whichever .exe runs the game (TS3.exe for Origin, TS3W.exe, with the W, for disc or Steam). This patch essentially applies the same workaround as the PowerShell script to the game .exe so it works on its own, with no need to run the patch or do anything else after the first time.
And no, EA hasn't fixed this problem yet.
