Drop Python 3.10 support, require Python 3.11+ (#9522)

Co-authored-by: pre-commit-ci-lite[bot] <117423508+pre-commit-ci-lite[bot]@users.noreply.github.com>

tests/integration/test_host_mode_empty_string_options.py

@@ -99,7 +99,7 @@ async def test_host_mode_empty_string_options(
         # Wait for initial states with timeout
         try:
             await asyncio.wait_for(states_received_future, timeout=5.0)
-        except asyncio.TimeoutError:
+        except TimeoutError:
             pytest.fail(
                 f"Did not receive states for all select entities. "
                 f"Expected keys: {expected_select_keys}, Received: {received_select_keys}"