Add weather caching, useless-tip redirect, clock widget, and IAM Bedrock auth

- Cache the latest fetched tomorrow weather and expose it via /api/system/weather/latest
- Add a header Clock widget showing date/time plus the cached weather summary
- Redirect useless-talk mentions from the weather bot to the useless-tips webhook
- Switch Bedrock auth from bearer token to standard IAM access key/secret

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

backend/app/api/system.py

@@ -3,6 +3,7 @@ import psutil
 from pydantic import BaseModel
 
 from app.core.scheduler import send_useless_tip, send_weather_laundry_notification
+from app.core.weather_cache import get_latest as get_latest_weather
 
 router = APIRouter(prefix="/api/system", tags=["system"])
 
@@ -61,3 +62,9 @@ async def test_useless_tip():
     """どうでもいいtips→Discord通知を手動で即時実行する（動作確認用）"""
     await send_useless_tip()
     return {"status": "sent"}
+
+
+@router.get("/weather/latest")
+async def get_latest_weather_data():
+    """直近で取得した明日の天気データを返す（未取得ならnull）"""
+    return get_latest_weather()