I believe that there is some confusion between the Windows Runtime and C++/CX going on here. C++/CX was the original Windows Runtime projection for C++, it is not the Windows Runtime itself.
C++/WinRT, the newer projection, works perfectly fine with the static runtime library, so using /MT or /MTd works fine. So my suggestion is to disable anything that was set for using the Windows Runtime and then open Solution Explorer. In Solution Explorer, right click on the project name or the references under the project name.
In this context menu, select "Manage NuGet Packages". In the window that appears, switch to browse and then search for Microsoft.Windows.CppWinRT, and install that package.
If the project is built once, then the generated files for the Windows Runtime can be found in the intermediate directory for the project.
The following shows a simple C++/WinRT source file that just creates an instance of the PackageManager runtime class.
#include <Windows.h>
#undef GetCurrentTime
#include <Unknwn.h>
#include <winrt/Windows.Foundation.h>
#include <winrt/Windows.Foundation.Collections.h>
#include <winrt/Windows.Management.Deployment.h>
#include <iostream>
int main()
{
winrt::init_apartment(winrt::apartment_type::multi_threaded);
auto package_manager = winrt::Windows::Management::Deployment::PackageManager{};
return 0;
}
The C++/WinRT documentation can be found easily, but it is a bit UWP centric.