bpo-45678: Add more `singledispatchmethod` tests (GH-29412)

In order to fix a bug in the 3.9 branch in #29394, more tests were added to
``test_functools.py`` to ensure that ``singledispatchmethod`` still correctly
wrapped a target method, even if the target method had already been wrapped by
 multiple other decorators. This PR brings the new tests into the 3.11 and 3.10
branches as well.

Lib/test/test_functools.py

@@ -2519,6 +2519,105 @@ class TestSingleDispatch(unittest.TestCase):
         self.assertEqual(A.static_func.__name__, 'static_func')
         self.assertEqual(A().static_func.__name__, 'static_func')
 
+    def test_double_wrapped_methods(self):
+        def classmethod_friendly_decorator(func):
+            wrapped = func.__func__
+            @classmethod
+            @functools.wraps(wrapped)
+            def wrapper(*args, **kwargs):
+                return wrapped(*args, **kwargs)
+            return wrapper
+
+        class WithoutSingleDispatch:
+            @classmethod
+            @contextlib.contextmanager
+            def cls_context_manager(cls, arg: int) -> str:
+                try:
+                    yield str(arg)
+                finally:
+                    return 'Done'
+
+            @classmethod_friendly_decorator
+            @classmethod
+            def decorated_classmethod(cls, arg: int) -> str:
+                return str(arg)
+
+        class WithSingleDispatch:
+            @functools.singledispatchmethod
+            @classmethod
+            @contextlib.contextmanager
+            def cls_context_manager(cls, arg: int) -> str:
+                """My function docstring"""
+                try:
+                    yield str(arg)
+                finally:
+                    return 'Done'
+
+            @functools.singledispatchmethod
+            @classmethod_friendly_decorator
+            @classmethod
+            def decorated_classmethod(cls, arg: int) -> str:
+                """My function docstring"""
+                return str(arg)
+
+        # These are sanity checks
+        # to test the test itself is working as expected
+        with WithoutSingleDispatch.cls_context_manager(5) as foo:
+            without_single_dispatch_foo = foo
+
+        with WithSingleDispatch.cls_context_manager(5) as foo:
+            single_dispatch_foo = foo
+
+        self.assertEqual(without_single_dispatch_foo, single_dispatch_foo)
+        self.assertEqual(single_dispatch_foo, '5')
+
+        self.assertEqual(
+            WithoutSingleDispatch.decorated_classmethod(5),
+            WithSingleDispatch.decorated_classmethod(5)
+        )
+
+        self.assertEqual(WithSingleDispatch.decorated_classmethod(5), '5')
+
+        # Behavioural checks now follow
+        for method_name in ('cls_context_manager', 'decorated_classmethod'):
+            with self.subTest(method=method_name):
+                self.assertEqual(
+                    getattr(WithSingleDispatch, method_name).__name__,
+                    getattr(WithoutSingleDispatch, method_name).__name__
+                )
+
+                self.assertEqual(
+                    getattr(WithSingleDispatch(), method_name).__name__,
+                    getattr(WithoutSingleDispatch(), method_name).__name__
+                )
+
+        for meth in (
+            WithSingleDispatch.cls_context_manager,
+            WithSingleDispatch().cls_context_manager,
+            WithSingleDispatch.decorated_classmethod,
+            WithSingleDispatch().decorated_classmethod
+        ):
+            with self.subTest(meth=meth):
+                self.assertEqual(meth.__doc__, 'My function docstring')
+                self.assertEqual(meth.__annotations__['arg'], int)
+
+        self.assertEqual(
+            WithSingleDispatch.cls_context_manager.__name__,
+            'cls_context_manager'
+        )
+        self.assertEqual(
+            WithSingleDispatch().cls_context_manager.__name__,
+            'cls_context_manager'
+        )
+        self.assertEqual(
+            WithSingleDispatch.decorated_classmethod.__name__,
+            'decorated_classmethod'
+        )
+        self.assertEqual(
+            WithSingleDispatch().decorated_classmethod.__name__,
+            'decorated_classmethod'
+        )
+
     def test_invalid_registrations(self):
         msg_prefix = "Invalid first argument to `register()`: "
         msg_suffix = (