[3.10] bpo-44594: fix (Async)ExitStack handling of __context__ (gh-27089) (GH-28730)

Make enter_context(foo()) / enter_async_context(foo()) equivalent to
`[async] with foo()` regarding __context__ when an exception is raised.

Previously exceptions would be caught and re-raised with the wrong
context when explicitly overriding __context__ with None..
(cherry picked from commit e6d1aa1ac6)

Co-authored-by: John Belmonte <john@neggie.net>

Automerge-Triggered-By: GH:njsmith

Lib/test/test_contextlib_async.py

@@ -552,6 +552,41 @@ class TestAsyncExitStack(TestBaseExitStack, unittest.TestCase):
         self.assertIsInstance(inner_exc, ValueError)
         self.assertIsInstance(inner_exc.__context__, ZeroDivisionError)
 
+    @_async_test
+    async def test_async_exit_exception_explicit_none_context(self):
+        # Ensure AsyncExitStack chaining matches actual nested `with` statements
+        # regarding explicit __context__ = None.
+
+        class MyException(Exception):
+            pass
+
+        @asynccontextmanager
+        async def my_cm():
+            try:
+                yield
+            except BaseException:
+                exc = MyException()
+                try:
+                    raise exc
+                finally:
+                    exc.__context__ = None
+
+        @asynccontextmanager
+        async def my_cm_with_exit_stack():
+            async with self.exit_stack() as stack:
+                await stack.enter_async_context(my_cm())
+                yield stack
+
+        for cm in (my_cm, my_cm_with_exit_stack):
+            with self.subTest():
+                try:
+                    async with cm():
+                        raise IndexError()
+                except MyException as exc:
+                    self.assertIsNone(exc.__context__)
+                else:
+                    self.fail("Expected IndexError, but no exception was raised")
+
 
 class TestAsyncNullcontext(unittest.TestCase):
     @_async_test