feat: initialize SQLAlchemy async database engine and session management with Neon-compatible configuration

backend/src/database.py

@@ -39,7 +39,7 @@ engine = create_async_engine(
     _db_url,
     echo=False,
     pool_pre_ping=True,
-    pool_recycle=120,        # More aggressive recycle (2 mins) for serverless environments
+    pool_recycle=300,        # Refreshes old connections every 5 min to prevent stale connection errors
     pool_size=10,
     max_overflow=5,
     connect_args={