feat(api): implement FastAPI lifespan with connection pooling

- Add connection pool config to SQLAlchemy async engine (pool_size=10, max_overflow=20, pool_pre_ping, pool_recycle)
- Implement Redis connection pool in CacheClient with initialize/close lifecycle
- Wire lifespan startup/shutdown to initialize and dispose pools
- Add dispose_engine() for graceful DB pool cleanup on shutdown

Closes CAR-550

Co-Authored-By: Paperclip <noreply@paperclip.ing>

src/cartsnitch_api/cache.py

@@ -1,26 +1,51 @@
 """Redis/DragonflyDB caching helpers."""
 
+import redis.asyncio as redis
+
 from cartsnitch_api.config import settings
 
 
 class CacheClient:
-    """Stub for Redis/DragonflyDB caching.
+    """Redis/DragonflyDB caching with connection pooling.
 
     Will be used for expensive queries: price trends, product comparisons.
     Cache invalidation via Redis pub/sub events from other services.
     """
 
     def __init__(self) -> None:
-        self.url = settings.redis_url
+        self._pool: redis.ConnectionPool | None = None
+        self._client: redis.Redis | None = None
+
+    async def initialize(self) -> None:
+        """Initialize the Redis connection pool."""
+        self._pool = redis.ConnectionPool.from_url(
+            settings.redis_url,
+            max_connections=20,
+            decode_responses=True,
+        )
+        self._client = redis.Redis(connection_pool=self._pool)
+
+    async def close(self) -> None:
+        """Close the Redis connection pool."""
+        if self._client:
+            await self._client.aclose()
+        if self._pool:
+            await self._pool.aclose()
 
     async def get(self, key: str) -> str | None:
-        # TODO: implement with redis-py async
-        return None
+        if not self._client:
+            return None
+        return await self._client.get(key)
 
     async def set(self, key: str, value: str, ttl_seconds: int = 300) -> None:
-        # TODO: implement with redis-py async
-        pass
+        if not self._client:
+            return
+        await self._client.set(key, value, ex=ttl_seconds)
 
     async def delete(self, key: str) -> None:
-        # TODO: implement with redis-py async
-        pass
+        if not self._client:
+            return
+        await self._client.delete(key)
+
+
+cache_client = CacheClient()