[libc] Update errno usage in integration tests. (#158147)

Instead of using libc_errno directly, include <errno.h> and use regular
"errno" in the code. (to verify that errno-as-an-interface works
properly).

This is the recipe prescribed in the libc/src/__support/libc_errno.h
header - let's actually follow it in the integration tests.

GitOrigin-RevId: d5aa5e33e6fd7c0d4035be5e7877f275b3205a36
6 files changed