Graphics Card Not Recognised by TS4

IncomingNazgul​  Sims 4 uses DirectX 9 or 11, depending on the graphics card and user settings.  So while DX12 is installed on your computer, and any system with Windows 11, it's not relevant to the game.

I don't see any obvious explanation in your dxdiag for the lag.  Do you use a third-party antivirus?  If so, try disabling it, temporarily of course, to see whether it helps loading times.  If it does, you can set exceptions for TS4_x64, TS4_DX9_x64, and TS4_Launcher_x64, or the Bin folder they're in.

Even if you don't think you have an antivirus running, please check in case one came pre-installed on your computer.

If that doesn't help, please create a new admin Windows account and try playing there.  Make it local, as in, don't link it to your Microsoft account or any email address.  You'll be able to launch Sims 4 without reinstalling anything, but your saves and other data won't be available.  The idea is to see whether some setting in your main account is the problem here.