feat(backend): Add Redis client with connection pooling

- Add RedisClient with async connection pool management
- Add cache operations (get, set, delete, expire, pattern delete)
- Add JSON serialization helpers for cache
- Add pub/sub operations (publish, subscribe, psubscribe)
- Add health check and pool statistics
- Add FastAPI dependency injection support
- Update config with Redis settings (URL, SSL, TLS)
- Add comprehensive tests for Redis client

Implements #17

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/core/config.py

@@ -39,6 +39,32 @@ class Settings(BaseSettings):
     db_pool_timeout: int = 30  # Seconds to wait for a connection
     db_pool_recycle: int = 3600  # Recycle connections after 1 hour
 
+    # Redis configuration (Syndarix: cache, pub/sub, Celery broker)
+    REDIS_URL: str = Field(
+        default="redis://localhost:6379/0",
+        description="Redis URL for cache, pub/sub, and Celery broker",
+    )
+
+    # Celery configuration (Syndarix: background task processing)
+    CELERY_BROKER_URL: str | None = Field(
+        default=None,
+        description="Celery broker URL (defaults to REDIS_URL if not set)",
+    )
+    CELERY_RESULT_BACKEND: str | None = Field(
+        default=None,
+        description="Celery result backend URL (defaults to REDIS_URL if not set)",
+    )
+
+    @property
+    def celery_broker_url(self) -> str:
+        """Get Celery broker URL, defaulting to Redis."""
+        return self.CELERY_BROKER_URL or self.REDIS_URL
+
+    @property
+    def celery_result_backend(self) -> str:
+        """Get Celery result backend URL, defaulting to Redis."""
+        return self.CELERY_RESULT_BACKEND or self.REDIS_URL
+
     # SQL debugging (disable in production)
     sql_echo: bool = False  # Log SQL statements
     sql_echo_pool: bool = False  # Log connection pool events