fix: repair broken tests and ensure Claude backend is used in integration tests

- Remove references to unimplemented get_benchmark_store from steward and
  tool tracking tests
- Fix steward test fixture calling async initialize_application synchronously
  by using sync register_household_members instead
- Rewrite tool tracking tests to assert actual logging behavior
- Change unit test fixture model from Tatlock to lorem-tester so unit tests
  don't require external services
- Add session-scoped _initialize_app fixture to run Claude health check,
  ensuring integration tests use Claude instead of falling back to Ollama
- Increase integration test timeouts from 30s to 120s to match OLLAMA_TIMEOUT
- Add Steward reasoning as ReasoningOutputItem in create_response_with_steward
  so <think> tags appear in chat completion responses
- Add test_tatlock_ollama_fallback to verify Ollama fallback path works

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

tests/conftest.py

@@ -2,6 +2,8 @@
 Shared test fixtures for all tests.
 Following FastAPI testing best practices.
 """
+import asyncio
+
 import pytest
 from fastapi.testclient import TestClient
 from httpx import AsyncClient, ASGITransport
@@ -9,11 +11,22 @@ from httpx import AsyncClient, ASGITransport
 from src.main import app
 
 
+@pytest.fixture(scope="session", autouse=True)
+def _initialize_app():
+    """
+    Run application lifespan (Claude health check, household registration, etc.)
+    once per test session. ASGITransport doesn't trigger lifespan events,
+    so we call it explicitly.
+    """
+    from src.core.startup import initialize_application
+    asyncio.run(initialize_application())
+
+
 @pytest.fixture
 def client() -> TestClient:
     """
     Synchronous test client for FastAPI.
-    
+
     Use for simple tests that don't require async.
     """
     return TestClient(app)
@@ -23,7 +36,7 @@ def client() -> TestClient:
 async def async_client() -> AsyncClient:
     """
     Async test client for FastAPI.
-    
+
     Use for testing async endpoints and streaming.
     """
     async with AsyncClient(
@@ -37,7 +50,7 @@ async def async_client() -> AsyncClient:
 def mock_chat_request() -> dict:
     """Standard chat completion request fixture."""
     return {
-        "model": "Tatlock",
+        "model": "lorem-tester",
         "messages": [
             {"role": "user", "content": "Hello, world!"}
         ],