Use LIBC_ERRNO_MODE_SYSTEM_INLINE instead as the default for the "public
packaging" (i.e. release mode) of an overlay build. The Bazel build has
already switched to use it by default in
5ccc734fa0355f971f8f515457a0bece33ab6642. This should be a safe change,
as LIBC_ERRNO_MODE_SYSTEM_INLINE works a drop-in (but simpler)
LIBC_ERRNO_MODE_SYSTEM replacement. Remove the associated code paths and
config settings.

Fixes issue #143454.

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

Summary:
The configs all need default values which targets then override. This
one was an empty string which made the logic report an error. The only
reason it wasn't a build failure was because of a stray `:`.

The definitions must match the previous declaration in errno.h.

This addresses the build error introduced in #98287 where
src/errno/errno.h is included instead of the system errno.h.

We instead move the declaration to libc_errno.h.

Rather than selecting the errno implementation based on the platform
which doesn't provide the necessary flexibility, make it configurable.

The errno value location is returned by `int *__llvm_libc_errno()` which
is a common design used by other C libraries.

This is a part of #97655.

Reverts llvm/llvm-project#98075

bots are broken

This is a part of #97655.

Summary:
The `errno` variable is expected to be `thread_local` by the standard.
However, the GPU targets do not support `thread_local` and implementing
that would be a large endeavor. Because of that, we previously didn't
provide the `errno` symbol at all. However, to build some programs we at
least need to be able to link against `errno`. Many things that would
normally set `errno` completely ignore it currently (i.e. stdio) but
some programs still need to be able to link against correct C programs.

For this purpose this patch exports the `errno` symbol as a simple
global. Internally, this will be updated atomically so it's at least not
racy. Externally, this will be on the user. I've updated the
documentation to state as such. This is required to get `libc++` to
build.