Power-to-methanol (PtMe) technologies and Carnot batteries are two promising approaches for large-scale energy storage. However, the current low efficiency and inadequate profitability of these two technologies, especially concerning green methanol production, pose challenges for their industrial implementation. One solution is to integrate these two technologies to augment the material and energy utilization efficiency through dynamic operational coordination and multi-energy production. This study systematically investigates the synergies of integrating CO2 energy storage (CES) and PtMe for combined heating, power, and methanol generation, aiming to enhance system's efficiency and economic viability. In this context, a novel hybrid energy-driven polygeneration system (CES-PtMe) is developed, featuring a highly integrated methanol production process and a newly proposed CES configuration with heating input and output capabilities. Detailed system simulations assess its performance under steady state, while nonlinear programming models are formulated for optimal storage sizing and energy scheduling considering fluctuating renewable energy. Various scenarios are set to examine the techno-economic potential of the CES-PtMe system, using renewable data from Gansu, China as a case study. The results indicate that the system can achieve a high efficiency of nearly 80% with a renewable penetration exceeding 77%. By incorporating optimal energy scheduling throughout the year, the system shows economic viability in the context of the current fossil energy market. While it has a limited ability to meet user energy demands, the proposed system retains economic benefits compared to standalone technologies.