@MomoDufrasne No new errors in the dxdiag means that DX9 is no longer the issue. It probably was initially—that's true for most new installs of Sims 3 when some other application hasn't already installed DX9—but when there's no error in the dxdiag, that points to a different problem.
On that note, have you ever had two EA/Origin accounts merged? If so, and the base game product code wasn't transferred properly, that would explain why the game doesn't open. In that case, you'd need to contact EA customer support and ask about the status of your base game code, not only whether it's present on your account but whether it's active and valid.
https://help.ea.com/en/contact-us/
If you've never had two accounts merged, this could also be a permissions issue. Try temporarily disabling your antivirus, if you use one, just long enough to test. If it works, you can set exceptions for Origin.exe, Sims3Launcher.exe, and TS3.exe.
If that doesn't help or you don't use a third-party program, create a new admin Windows account and try to play in that. Make it a local account, as in, don't sign into Microsoft, and don't sync with any other services you normally use. You'll be able to sign into your existing Origin account and shouldn't have to redownload anything.
DtsApo4Service.exe is part of a sound enhancement service, so you can try shutting it down (and anything with a similar name) through the Task Manager before launching the game. It doesn't usually conflict with Sims 3, but there's no harm in testing. If you accidentally kill the wrong process and it doesn't restart automatically, just reboot your computer.
I doubt installing Windows 11 would help unless your Windows 10 install is corrupt in some way. But a repair install should address almost all Windows-related issues if it comes to that.