[libc++][C++03] Use `__cxx03/` headers in C++03 mode (#109002)

This patch implements the forwarding to frozen C++03 headers as
discussed in
https://discourse.llvm.org/t/rfc-freezing-c-03-headers-in-libc. In the
RFC, we initially proposed selecting the right headers from the Clang
driver, however consensus seemed to steer towards handling this in the
library itself. This patch implements that direction.

At a high level, the changes basically amount to making each public
header look like this:

```
// inside <vector>
#ifdef _LIBCPP_CXX03_LANG
#  include <__cxx03/vector>
#else
  // normal <vector> content
#endif
```

In most cases, public headers are simple umbrella headers so there isn't
much code in the #else branch. In other cases, the #else branch contains
the actual implementation of the header.