Move reversing slice of middleware apps into the cache (#9170)

(cherry picked from commit eacf2e0)

CHANGES/9170.misc.rst

@@ -0,0 +1 @@
+9158.misc.rst

aiohttp/web_app.py

@@ -84,7 +84,7 @@ def _build_middlewares(
     handler: Handler, apps: Tuple["Application", ...]
 ) -> Callable[[Request], Awaitable[StreamResponse]]:
     """Apply middlewares to handler."""
-    for app in apps:
+    for app in apps[::-1]:
         for m, _ in app._middlewares_handlers:  # type: ignore[union-attr]
             handler = update_wrapper(partial(m, handler=handler), handler)  # type: ignore[misc]
     return handler
@@ -545,7 +545,7 @@ async def _handle(self, request: Request) -> StreamResponse:
 
             if self._run_middlewares:
                 if not self._has_legacy_middlewares:
-                    handler = _build_middlewares(handler, match_info.apps[::-1])
+                    handler = _build_middlewares(handler, match_info.apps)
                 else:
                     for app in match_info.apps[::-1]:
                         for m, new_style in app._middlewares_handlers:  # type: ignore[union-attr]