Avoid running final writes in executor in test (#84679)

tests/common.py

@@ -1165,13 +1165,13 @@ def mock_storage(data=None):
 
         # Route through original load so that we trigger migration
         loaded = await orig_load(store)
-        _LOGGER.info("Loading data for %s: %s", store.key, loaded)
+        _LOGGER.debug("Loading data for %s: %s", store.key, loaded)
         return loaded
 
-    def mock_write_data(store, path, data_to_write):
+    async def mock_write_data(store, path, data_to_write):
         """Mock version of write data."""
         # To ensure that the data can be serialized
-        _LOGGER.info("Writing data to %s: %s", store.key, data_to_write)
+        _LOGGER.debug("Writing data to %s: %s", store.key, data_to_write)
         raise_contains_mocks(data_to_write)
         data[store.key] = json.loads(json.dumps(data_to_write, cls=store._encoder))
 
@@ -1184,7 +1184,7 @@ def mock_storage(data=None):
         side_effect=mock_async_load,
         autospec=True,
     ), patch(
-        "homeassistant.helpers.storage.Store._write_data",
+        "homeassistant.helpers.storage.Store._async_write_data",
         side_effect=mock_write_data,
         autospec=True,
     ), patch(