[clang] Separate Intel ADC instrinsics from ADX intrinsics (#75992)

See https://github.com/llvm/llvm-project/pull/75711 for discussion.

As a summary from the PR above, `<adxintrin.h>` includes adc intrinsics
and adx intrinsics.
To support MSVC STL we need to expose the adc intrinsics inside the
currently proposed `<intrin0.h>` header.
Move the processor agnostic adc intrinsics into a separate file that can
be included from `<immintrin.h>` and the currently proposed
`<intrin0.h>`.