lib/newlib: revert treatment of libc files as system includes

The solution from #14312 of using -isystem to prioritize the position of
the libc directory bypasses the effect of -ffreestanding with respect to
libc symbols expected to be present in a non-hosted environment.

Further, it breaks C++ with the ARM Embedded toolchain as the system
fails to find the right file with #include_next.

Use a more fine-grained solution that explicitly includes the underlying
newlib header required for <inttypes.h> support before moving on to
include the next available one, whether system or non-system.

Closes #17564

Backport: 96c1b051
Signed-off-by: Peter Bigot <peter.bigot@nordicsemi.no>