[3.13] gh-122559: Synchronize C and Python implementation of the io module about pickling (GH-122628) (GH-133381)

In the C implementation, remove __reduce__ and __reduce_ex__ methods
that always raise TypeError and restore __getstate__ methods that always
raise TypeErrori.

This restores fine details of the pre-3.12 behavior and unifies
both implementations.
(cherry picked from commit e9253ebf74433de5ae6d7f1bce693a3a1173b3b1)