Before you try a manual install, I’d check if the Path in the system’s environment variables is correctly configured for your system.
Given that there’s always one shared host that moves forward, it will either pick the x86 or the x64 version on your machine. This issue of not picking the right one might happen if you install multiple/different versions.
Run the where.exe dotnet command to see where the host is looking for the SDK (it’s the first entry returned). If you’re on a x64 machine, you want to have C:\Program Files\dotnet listed first.
If it’s not, edit the Path system’s environment variable to have the location you want showing up higher. Doing that should fix the issue of the SDK versions you installed not showing up when you run dotnet --info.
See The latest installed .NET SDK not found for complete instructions.