[libc++] Granularize __mutex_base

This also updates the moved code to the current style. (i.e. `_VSTD` -> `std`, `_LIBCPP_INLINE_VISIBILITY` -> `_LIBCPP_HIDE_FROM_ABI`, clang-format).

Reviewed By: Mordante, #libc, EricWF

Spies: arichardson, libcxx-commits, mikhail.ramalho

Differential Revision: https://reviews.llvm.org/D146228

GitOrigin-RevId: e655d8a54880cf550567dda0e9a1a33f6ee98df5