As a crucial carrier for supporting the implementation of the "dual carbon" goals and empowering rural revitalization, rural microgrids can effectively enhance overall system operational efficiency by integrating distributed energy with traditional power generation resources. To this end, this paper proposes a optimal operation strategy for source-grid-load-storage in rural microgrids based on an improved twin delayed deep deterministic policy gradient (TD3) algorithm. Firstly, an optimal operation model for rural microgrids incorporating biogas is constructed by comprehensively considering operating costs and renewable energy utilization. Secondly, a compound assessment scored attention-weighted critic(CASA-Critic)is designed to dynamically extract and focus on key state features, thereby enhancing the evaluation accuracy of the value network. Then, a dynamic perception strategy is introduced to adaptively adjust the intensity of action exploration based on the temporal progression and environmental state uncertainties during training, improving the balance between exploration and exploitation. Finally, simulation analysis is conducted based on a typical rural microgrids source-grid-load-storage operation scenario. The results demonstrate that, compared to optimization strategies based on other deep reinforcement learning, the proposed method exhibits better convergence and optimization performance, while also showing significant superiority in improving system operational economy and promoting renewable energy accommodation.