VS Code with Clang-Cl under Windows: Build Error

Question

I want to use Clang-Cl under Windows to build my projects. As generator I use Ninja and my IDE is Visual Studio Code to which I switched recently. VS Code uses the compiler kit

{
 "name": "Clang 9.0.0 für MSVC mit Visual Studio Build Tools 2019 Release (amd64)",
 "visualStudio": "8b490674",
 "visualStudioArchitecture": "amd64",
 "compilers": {
   "C": "C:\\LLVM\\bin\\clang-cl.exe",
   "CXX": "C:\\LLVM\\bin\\clang-cl.exe"
 }
}, ...

Cmake Tools Extension is now successfully configuring my project, the problem I have is that the build stops due to too many errors. I am building a debug build, so I am not sure if the compiler kit is already wrong because it says something of Release. Switching the Architecture in the kit to "visualStudioArchitecture": "x64" does nothing. Here is a list of errors I get

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\vcruntime_exception.h(28,5): error: unknown type name 'bool'; did you mean 'Bool'?

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\vcruntime_exception.h(32,11): error: must use 'struct' tag to refer to type '__std_exception_data'

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\vcruntime_exception.h(44,1): error: unknown type name 'namespace'

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\vcruntime_exception.h(44,14): error: expected ';' after top level declarator

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\exception(205,81): error: expected function body after function declarator

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\limits(23,1): error: expected ';' after top level declarator

C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\include\limits(23,1): error: unknown type name 'namespace'

I do not have any more settings made than choosing the compiler kit. Has anyone an idea what could be missing?

Here is the final error from VS Code

[build] fatal error: too many errors emitted, stopping now [-ferror-limit=]
[build] 20 errors generated.
[build] ninja: build stopped: subcommand failed.
[build] Der Build wurde mit dem Exitcode 1 abgeschlossen.

I also tried CLion, there's the same problem but the error output looks a bit different

fatal error: too many errors emitted, stopping now [-ferror-limit=]
20 errors generated.
NMAKE : fatal error U1077: "C:\LLVM\bin\clang-cl.exe": Rückgabe-Code "0x1"
Stop.
NMAKE : fatal error U1077: ""C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\bin\HostX64\x64\nmake.exe"": Rückgabe-Code "0x2"
Stop.
NMAKE : fatal error U1077: ""C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Tools\MSVC\14.26.28801\bin\HostX64\x64\nmake.exe"": Rückgabe-Code "0x2"
Stop.