The new Windows Driver Kit extension is an extension not an installed component. You install it, as documented, by using the Extensions menu item in VS2022.
Also, as long as you are modifying how you use these tools, you should consider using the nuget WDK/SDK components rather than installing them into VS.
I wrote up a brief description of how to use the nuget components here: Announcing the WDK NuGet: A New Way to Develop Drivers on WIndows - #20 by Mark_Roddy