[PR #10977/48f5324b backport][3.12] Fix flakey test_aiohttp_request_ctx_manager_close_sess_on_error test (#10980)

Co-authored-by: J. Nick Koston <[email protected]>

Author: patchback[bot]

tests/test_client_functional.py

@@ -3393,6 +3393,9 @@ async def handler(request):
             pass
 
     assert cm._session.closed
+    # Allow event loop to process transport cleanup
+    # on Python < 3.11
+    await asyncio.sleep(0)
 
 
 async def test_aiohttp_request_ctx_manager_not_found() -> None: