The global transition toward net zero emissions has accelerated the integration of distributed generators (DGs), particularly renewable energy sources (RESs), energy storage systems, plug-in electric vehicles (PEVs), and fuel-cell electric vehicles (FEVs). Therefore, we propose a decentralized energy management model tailored to the operational dynamics of a community of independent microgrids (MGs) at the transmission level, integrated with DGs, PEVs, FEVs, and hydrogen-based technologies, forming power- and hydrogen-based microgrids (P&HMGs). Managed by a third-party aggregator, P&HMGs strategically participate in the wholesale electricity market (WEM) by consolidating bids and offers. The WEM operates between generators and suppliers. The participating generators in WEM are connected to the transmission level, including power plants and large-scale RESs. The strategic behavior of P&HMGs is modeled using bi-level programming that unveils the potential of P&HMGs to synergize and participate in WEM as a price-maker. Moreover, to cope with the data privacy of P&HMGs and improve the scalability and security of MGs, a fast alternating direction method of multipliers (ADMM) running on a mobile edge computing (MEC) system is proposed as a decentralized energy management approach. Further, a bidirectional long short-term memory (BiLSTM) network considering robust optimization is presented to control the intermittency of electrical load and RESs. The results obtained from case studies confirm a considerable reduction in operation costs in light of the proposed model.