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/core/scheduler.py

@@ -22,6 +22,7 @@ from app.core.config import (
 from app.core.llm import complete
 from app.core.notify import send_discord_message
 from app.core.weather import fetch_tomorrow_weather, judge_laundry
+from app.core.weather_cache import set_latest
 
 logger = logging.getLogger(__name__)
 
@@ -37,6 +38,7 @@ async def send_weather_laundry_notification() -> None:
         weather_data = await fetch_tomorrow_weather(WEATHER_AREA_CODE, WEATHER_AREA_KEYWORD)
         judgement, reason = judge_laundry(weather_data["weather"], weather_data["pop"])
         pop_text = f"{weather_data['pop']}%" if weather_data["pop"] is not None else "不明"
+        set_latest(weather_data["weather"], weather_data["pop"], judgement, reason)
 
         content = await _generate_message(weather_data["weather"], pop_text, judgement, reason)
         await send_discord_message(DISCORD_WEBHOOK_URL, content)