Water supply systems (WSS) are energy-intensive and well-suited for demand-side management because of controllable operations and significant water storage capacity. Due to the current challenges facing the water sector, particularly rising energy prices, improving the operational efficiency of WSS is paramount. Water utilities willing to participate in demandside management programs can reduce their energy costs by implementing cost-effective load management strategies. By shifting pumping operations, incorporating on-site renewable energy, and leveraging storage systems, utilities can reduce energy costs while ensuring reliable water supply. This work introduces a Model Predictive Control (MPC) framework to optimize WSS operations through integrated resource management (exchanges with the grid, load management, storage systems, local generation) to improve energy and cost efficiency. This framework incorporates predicter models functioning as smart predictive digital twins, representing WSS hydraulic behavior and battery dynamics, combined with nonlinear programming techniques. This approach enables the resolution of complex optimization problems within feasible computational timeframes, yielding practical and effective solutions. In a real-world WSS case study, the approach demonstrated the potential to reduce energy costs by 32% and provided flexibility benefits to the power grid. Compared to conventional practices, this framework enabled peak power reductions exceeding 40% and achieved flexibility factors above 55%, underscoring the significant role of WSS in providing flexibility to the grid.