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/database.py

@@ -6,7 +6,14 @@ from sqlalchemy.ext.asyncio import AsyncSession, async_sessionmaker, create_asyn
 
 from cartsnitch_api.config import settings
 
-engine = create_async_engine(settings.database_url, echo=False)
+engine = create_async_engine(
+    settings.database_url,
+    echo=False,
+    pool_size=10,
+    max_overflow=20,
+    pool_pre_ping=True,
+    pool_recycle=3600,
+)
 async_session_factory = async_sessionmaker(engine, class_=AsyncSession, expire_on_commit=False)
 
 
@@ -14,3 +21,8 @@ async def get_db() -> AsyncGenerator[AsyncSession, None]:
     """FastAPI dependency that yields an async DB session."""
     async with async_session_factory() as session:
         yield session
+
+
+async def dispose_engine() -> None:
+    """Dispose the database engine, closing all pooled connections."""
+    await engine.dispose()