In https://github.com/llvm/llvm-project/pull/176903, `#include
<__configuration/compiler.h>` is moved into the
`#ifdef _cplusplus` clause, so `_LIBCPP_COMPILER_CLANG_BASED` is no
longer set for C compiles. This causes a regression internally, where
when C compiles includes stdatomic.h, they no longer get the
corresponding C header.
C++ stdlib headers "shouldn't" be on the search patch for C compile, but
we do and so do lots of other people, so libc++ tends to support that.
This include_next for a C compile should be unconditional, not
conditional upon being Clang.
09f8f22a64