posix: pthread: mitigate include order sensitivity

Previously, the `posix_internal.h` header needed to be exposed
to the application because we had non-trivial details for
most posix types (pthread, mutex, cond, ...). Since most of
those have been simplified to a typedef'ed integer, we
no longer need to expose that header to the applicaiton.

Additionally, it means that we can adopt normalized
header order in posix.

Additionally, keep more implementation details hidden
and prefer the static keyword on internal symbols where
possible.

Signed-off-by: Christopher Friedt <cfriedt@meta.com>