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This research presents an interconnected operation model that integrates carbon capture and storage (CCS) with power to gas (P2G), tackles the challenges encountered by integrated electricity-natural gas systems (IEGS) in terms of energy consumption and achieving low-carbon economic operations, and formulates a DRL-based, physically model-free energy optimization management strategy for IEGS, designed to lower operational costs and carbon emissions. Initially, the CCS-P2G interconnected IEGS system undergoes mathematical modeling. Subsequently, the system's uncertainty in optimal scheduling is formulated as a Markov decision process, with the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm facilitating real-time scheduling decisions. Comparative analysis across various scenarios demonstrates that the model offers superior low-carbon economic benefits and enhanced environmental sustainability. Further analysis validates that the optimized scheduling strategy proposed herein advantages in achieving low-carbon financial objectives, convergence speed, and system learning performance, as evidenced by training the model with historical data and the comparative analysis of the DQN and DDPG algorithms. • "Integrates CCS and P2G in IEGS for optimal renewable use." • "Reduces wind and solar curtailment effectively." • "Enhances system's low-carbon economy significantly." • "Utilizes surplus renewable energy for hydrogen production." • "Demonstrates CCS-P2G synergy in minimizing carbon emissions." [ABSTRACT FROM AUTHOR]