C# csproj <None> tool, VS_TOOL_OVERRIDE not working

I’m using CMake to convert an old project having C# project files, and in them there are a couple file using the <None …> tool, effectively disabling them from build. I saw the VS_TOOL_OVERRIDE property (https://cmake.org/cmake/help/latest/prop_sf/VS_TOOL_OVERRIDE.html) which sais it should allow me to override the tool but it doesn’t work for .cs and .resx files (a couple of those are set to None in the old csproj I’m converting to CMake).
How can I set the None tool for these files?

Wild guess, but perhaps setting their source property HEADER_FILE_ONLY to TRUE could help.

Unfortunately no, if I set HEADER_FILE_ONLY then it becomes a <ClInclude>...</ClInclude> node always (regardless of the extension).

I would have said, setting the LANGUAGE to NONE should be working. Just like on the project command.

But this property only allows enabled languages.
So I guess you have to create a feature request, if there are no other suggestions.