[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 e9253ebf74)

Lib/test/test_io.py

@@ -1349,6 +1349,28 @@ class CommonBufferedTests:
         with self.assertRaises(AttributeError):
             buf.raw = x
 
+    def test_pickling_subclass(self):
+        global MyBufferedIO
+        class MyBufferedIO(self.tp):
+            def __init__(self, raw, tag):
+                super().__init__(raw)
+                self.tag = tag
+            def __getstate__(self):
+                return self.tag, self.raw.getvalue()
+            def __setstate__(slf, state):
+                tag, value = state
+                slf.__init__(self.BytesIO(value), tag)
+
+        raw = self.BytesIO(b'data')
+        buf = MyBufferedIO(raw, tag='ham')
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
+            with self.subTest(protocol=proto):
+                pickled = pickle.dumps(buf, proto)
+                newbuf = pickle.loads(pickled)
+                self.assertEqual(newbuf.raw.getvalue(), b'data')
+                self.assertEqual(newbuf.tag, 'ham')
+        del MyBufferedIO
+
 
 class SizeofTest:
 
@@ -3932,6 +3954,28 @@ class TextIOWrapperTest(unittest.TestCase):
         f.write(res)
         self.assertEqual(res + f.readline(), 'foo\nbar\n')
 
+    def test_pickling_subclass(self):
+        global MyTextIO
+        class MyTextIO(self.TextIOWrapper):
+            def __init__(self, raw, tag):
+                super().__init__(raw)
+                self.tag = tag
+            def __getstate__(self):
+                return self.tag, self.buffer.getvalue()
+            def __setstate__(slf, state):
+                tag, value = state
+                slf.__init__(self.BytesIO(value), tag)
+
+        raw = self.BytesIO(b'data')
+        txt = MyTextIO(raw, 'ham')
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
+            with self.subTest(protocol=proto):
+                pickled = pickle.dumps(txt, proto)
+                newtxt = pickle.loads(pickled)
+                self.assertEqual(newtxt.buffer.getvalue(), b'data')
+                self.assertEqual(newtxt.tag, 'ham')
+        del MyTextIO
+
 
 class MemviewBytesIO(io.BytesIO):
     '''A BytesIO object whose read method returns memoryviews