Fix race condition with request handlers on shutdown (#8271)

(cherry picked from commit e0d9d3a)

CHANGES/8271.bugfix.rst

@@ -0,0 +1 @@
+Fixed a race condition with incoming connections during server shutdown -- by :user:`Dreamsorcerer`.

aiohttp/web_runner.py

@@ -307,6 +307,9 @@ async def cleanup(self) -> None:
             await site.stop()
 
         if self._server:  # If setup succeeded
+            # Yield to event loop to ensure incoming requests prior to stopping the sites
+            # have all started to be handled before we proceed to close idle connections.
+            await asyncio.sleep(0)
             self._server.pre_shutdown()
             await self.shutdown()