Sustainable and clean multi-energy systems have been hybrid coordinated in microgrid (MG) to fulfill regional multi-energy users economically, but shortages and surpluses still exist. The growth of win-win energy sharing between MGs attracts attention to smart information center (SIC) concept in MGs community, which facilitates sustainable solutions across three key objectives: lower carbon emission, sufficient utilization, and long-term cooperation. This paper designs a two-stage decision framework for day-ahead operations of SIC, where the first stage minimizes the total cost (i.e. operational cost and carbon emission cost) by the proposed multi-energy intra-scheduling and inter-sharing model (MIIM) and the second stage implements the smart cost-saving redistribution model (SCRM) to stimulate MGs in long-term joining of energy sharing. The extended alternating direction multipliers method algorithm (E-ADMM) is developed to protect the privacy of MGs data while approximating the optimal solution of MIIM. The case study proves that a) demand response and energy sharing in MIIM result in cost savings of 2.01% for carbon emissions and 7.25% for total operations; b) renewable energy has been fully utilized and the total multi-energy loss has been avoided nearly 92.22% in MIIM; c) the asymmetric Nash bargaining approach fits the SCRM with incentive cooperation, whereby those who contribute more gain a higher share; d) the optimal gap of E-ADMM is less than 0.2% by iterated insensitive decision result from each MG, which computes in polynomial time when the scale of MG increases; e) the two-stage framework performs better with more heterogeneity of MGs. Furthermore, we provide valuable insights for guidance and models with worldwide generalization potential.