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.
04081caa09