feat: add Sentry error monitoring and tracing to FastAPI backend

- Install sentry-sdk[fastapi] with auto-enabled FastAPI + Anthropic
  integrations
- Init before app = FastAPI() with env-aware sample rates
  (100% dev, 20% prod)
- Filter /health endpoint from traces to reduce noise
- Add SENTRY_DSN to config settings

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

backend/app/core/config.py

@@ -118,6 +118,9 @@ class Settings(BaseSettings):
         """Check if any AI provider is configured."""
         return self.ANTHROPIC_API_KEY is not None or self.GOOGLE_AI_API_KEY is not None
 
+    # Monitoring
+    SENTRY_DSN: Optional[str] = None
+
     # Deployment – auto-seed test data on PR environments
     SEED_ON_DEPLOY: bool = False