[libc++] Revert "Protect users from relying on detail headers" & related changes

This commit reverts 5aaefa51 (and also partly 7f285f48e77 and b6d75682f9,
which were related to the original commit). As landed, 5aaefa51 had
unintended consequences on some downstream bots and didn't have proper
coverage upstream due to a few subtle things. Implementing this is
something we should do in libc++, however we'll first need to address
a few issues listed in https://reviews.llvm.org/D106124#3349710.

Differential Revision: https://reviews.llvm.org/D120683

NOKEYCHECK=True
GitOrigin-RevId: 368faacac7525e538fa6680aea74e19a75e3458d
diff --git a/src/fallback_malloc.cpp b/src/fallback_malloc.cpp
index 9db431e..1d6c380 100644
--- a/src/fallback_malloc.cpp
+++ b/src/fallback_malloc.cpp
@@ -8,7 +8,7 @@
 
 #include "fallback_malloc.h"
 
-#include "threading_support.h"
+#include <__threading_support>
 #ifndef _LIBCXXABI_HAS_NO_THREADS
 #if defined(__ELF__) && defined(_LIBCXXABI_LINK_PTHREAD_LIB)
 #pragma comment(lib, "pthread")