Simplify session response fields by removing redundant new_session in deprecated path

The deprecated behavior path was setting both new_session=True and unsaved=True,
which was redundant. The unsaved field alone is sufficient to indicate that this
is deprecated behavior returning an unpersisted session.

Author: abrookins

agent_memory_server/api.py

@@ -386,7 +386,6 @@ async def get_working_memory(
                 "GET /v1/working-memory/{session_id} will return 404 for missing sessions in version 1.0. "
                 "Use get_or_create_working_memory client method instead."
             )
-            new_session = True
             unsaved = True
             # Create empty working memory but DO NOT persist it
             working_mem = WorkingMemory(

tests/test_api.py

@@ -437,8 +437,7 @@ async def test_delete_memory(self, client, session):
         # Should return 200 with unsaved session (deprecated behavior for old clients)
         assert response.status_code == 200
         data = response.json()
-        assert data["new_session"] is True  # Session was created
-        assert data["unsaved"] is True  # But not persisted (deprecated behavior)
+        assert data["unsaved"] is True  # Not persisted (deprecated behavior)
         assert len(data["messages"]) == 0  # Empty session
         assert len(data["memories"]) == 0