fix: send notifications on message not streaming

src/a2a/server/request_handlers/default_request_handler.py

@@ -55,6 +55,7 @@
     TaskState.rejected,
 }
 
+
 @trace_class(kind=SpanKind.SERVER)
 class DefaultRequestHandler(RequestHandler):
     """Default request handler for all incoming requests.
@@ -249,6 +250,11 @@ async def on_message_send(
                     InternalError(message='Task ID mismatch in agent response')
                 )
 
+            if self._push_notifier and task_id:
+                latest_task = await result_aggregator.current_result
+                if isinstance(latest_task, Task):
+                    await self._push_notifier.send_notification(latest_task)
+
         finally:
             if interrupted:
                 # TODO: Track this disconnected cleanup task.