This is the first step in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450

This is a part of #97655.

Reverts llvm/llvm-project#98075

bots are broken

This is a part of #97655.

reland of https://github.com/llvm/llvm-project/pull/98215

Additionally adds proxy headers for FILE and the fopencookie types

The arm32 build has been failing due to redefinitions of the off_t type.
This patch fixes this by moving off_t to a proper proxy header. To do
this, it also moves stdio macros to a proxy header to hopefully avoid
including this proxy header alongside this public stdio.h.

Summary:
The `puts` function consists of an initial write and then another write
to append the newline. When executing code in parallel, it is possible
for these writes to becomes disjointed. This code adds an explicit lock
call to ensure that the string is always appended by the newline as the
users expects.

Wasn't sure if this required a test as it would be difficult since
reproducing it would be flaky.

This is step 4 of
https://discourse.llvm.org/t/rfc-customizable-namespace-to-allow-testing-the-libc-when-the-system-libc-is-also-llvms-libc/73079

For whatever reason, the CMake did not like having the `generic_`
version live in the same directory. This patch pushes them to a new
directory, which is probably clearer anyway.

Reviewed By: michaelrj

Differential Revision: https://reviews.llvm.org/D157544