[libc++] Remove the dead code in  stdatomic.h in frozen C++03 mode (#188346)

Fixes #187384

Assisted-by: Claude Code

Signed-off-by: mlevine55 <mlevine55@bloomberg.net>
NOKEYCHECK=True
GitOrigin-RevId: e80b46efc500d603e0f10f95714765fc406bc625