Coordinating Vehicle to Everything (V2X) services across multiple building microgrids remains challenging due to scalability limitations, lack of convergence guarantees, and inadequate battery degradation consideration. This paper develops a hierarchical Cognitive Digital Twin (CDT) framework for coordinated V2X services across networked building microgrids. The framework comprises local building digital twins managing individual operations and a central coordinator orchestrating peer to peer (P2P) energy trading through a distributed consensus algorithm. A Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm with physics informed battery degradation constraints is developed, with theoretical analysis establishing convergence to an ϵ-local Nash equilibrium under standard assumptions. Simulations on a modified IEEE 33-bus system with 3–20 building microgrids, validated using real world datasets (UK-DALE, ACN-Data, Pecan Street), demonstrate 47.7% ± 3.2% reduction in daily operating costs compared to state of the art methods. Statistical analysis over 10 independent runs (p < 0.001) validates the effectiveness of the proposed approach.