[libc++][ci] Add a test configuration with an incomplete sysroot (#107089)

When bringing up a new cross compiler from scratch, we build
libunwind/libcxx in a setup where the toolchain is incomplete and unable
to perform the normal linker checks; this requires a few special cases
in the CMake files.

We simulate that scenario by removing the libc++ headers, libunwind and
libc++ libraries from the installed toolchain.

We need to set CMAKE_CXX_COMPILER_WORKS since CMake fails to probe the
compiler. We need to set CMAKE_CXX_COMPILER_TARGET, since LLVM's
heuristics fail when CMake hasn't been able to probe the environment
properly. (This is normal; one has to set those options when setting up
such a toolchain from scratch.)

This adds CI coverage for these build scenarios, which otherwise seldom
are tested by some build flow (but are essential when setting up a cross
compiler from scratch).

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