Just the same error as before occurs again. Screenshots 19 and 20 are the PowerShell results you asked for.
I thought I'd also attach a screenshot of the appwiz.cpl (Screenshot 22). The first time I tried I only ticked the upper folder and I thought it didn't help because the 2 lower folders weren't selected. But checking them as well on the second try didn't change anything, unfortunately. ☹️
In the screenshot you can also see the newer .NET version I've got on my laptop and which bits of it are checked - maybe this could help.
@piperofpeace Sims 3 doesn't use .NET Framework 4.x, so in theory, none of those components should matter. You can check them anyway if you want; if it doesn't help, you can uncheck the boxes again. This won't do any harm.
One other simple step to try is reinstalling the VC++ 2005 x86 runtime, which Sims 3 uses. The errors in your dxdiag aren't typically associated with that—they've been almost exclusively related to the DX9 error—but the runtimes do all need to work together. Hit Windows key-i, select Apps, scroll down to the Microsoft Visual C++ Redistributables, click on the 2005 version (it won't say x86, but that's what it is), and uninstall it. You can download a fresh copy from Microsoft:
https://www.microsoft.com/en-us/download/details.aspx?id=26347
You only need the x86 version, not the other two. Install it, restart your computer, and try again to play.
If that doesn't help, what might be useful here is a repair install of Windows. Reinstalling .NET 3.5 and DirectX 9 should have fixed this issue, and the fact that they didn't makes the repair install the logical next step. Here's how to run one:
https://www.elevenforum.com/t/repair-install-windows-11-with-an-in-place-upgrade.418/
This shouldn't delete any data, but if you get to step 14 and are NOT asked to keep personal files and apps, back out and start over.
Once the repair install is complete, please run the DX9 installer (yet again), just to be thorough. Make sure you're actually installing the runtime—the first step is just extracting it, and a few players have thought that was sufficient and never finished the install process. If you want to double-check your work, compare what you've done to these instructions I posted earlier:
https://answers.ea.com/t5/Technical-Issues-PC/Sims-3-launcher-won-t-open/m-p/10711778#M247861
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