[libc++][C++03] Remove some of the C++03-specific C wrapper headers (#163772)

`include_next` doesn't work very well with the C++03 headers and
modules. Since these specific headers are very self-contained there
isn't much of a reason to split them into C++03/non-C++03 headers, so
let's just remove them. The few C wrapper headers that aren't as
self-contained will be refactored in a separate patch.

GitOrigin-RevId: 44331d25949302c3898b71fa5aceaea3d49248b5