Remove duplicate call to sync_metadata inside DagFileProcessorManager (…

…apache#15121)

`_process_message` already calls sync_metadata if it's a DagParsingStat,
so there's no need to call it again.  This isn't expensive, but no point
doing it

I've also added a runtime check to ensure this function is only used in
sync mode, which makes the purpose/logic used in this function clearer.

airflow/utils/dag_processing.py

@@ -313,16 +313,17 @@ def wait_until_finished(self) -> None:
         """Waits until DAG parsing is finished."""
         if not self._parent_signal_conn:
             raise ValueError("Process not started.")
+        if self._async_mode:
+            raise RuntimeError("wait_until_finished should only be called in sync_mode")
         while self._parent_signal_conn.poll(timeout=None):
             try:
                 result = self._parent_signal_conn.recv()
             except EOFError:
-                break
+                return
             self._process_message(result)
             if isinstance(result, DagParsingStat):
-                # In sync mode we don't send this message from the Manager
-                # until all the running processors have finished
-                self._sync_metadata(result)
+                # In sync mode (which is the only time we call this function) we don't send this message from
+                # the Manager until all the running processors have finished
                 return
 
     @staticmethod