[3.11] gh-111085: Fix invalid state handling in TaskGroup and Timeout (GH-111111) (GH-111172)

asyncio.TaskGroup and asyncio.Timeout classes now raise proper RuntimeError
if they are improperly used.

* When they are used without entering the context manager.
* When they are used after finishing.
* When the context manager is entered more than once (simultaneously or
  sequentially).
* If there is no current task when entering the context manager.

They now remain in a consistent state after an exception is thrown,
so subsequent operations can be performed correctly (if they are allowed).

(cherry picked from commit 6c23635f2b)

Co-authored-by: Serhiy Storchaka <storchaka@gmail.com>
Co-authored-by: James Hilton-Balfe <gobot1234yt@gmail.com>

Lib/test/test_asyncio/utils.py

@@ -612,3 +612,18 @@ def mock_nonblocking_socket(proto=socket.IPPROTO_TCP, type=socket.SOCK_STREAM,
     sock.family = family
     sock.gettimeout.return_value = 0.0
     return sock
+
+
+async def await_without_task(coro):
+    exc = None
+    def func():
+        try:
+            for _ in coro.__await__():
+                pass
+        except BaseException as err:
+            nonlocal exc
+            exc = err
+    asyncio.get_running_loop().call_soon(func)
+    await asyncio.sleep(0)
+    if exc is not None:
+        raise exc