Shared energy storage (SES) represents a transformative approach to advancing sustainable energy systems through improved resource utilization and renewable energy integration. In order to enhance the economic benefits of energy storage and prosumers, as well as to increase the consumption rate of renewable energy, this paper proposes a bilevel optimization model for multi-prosumer power complementarity based on SES. The upper level is the long-term energy storage capacity configuration optimization, aiming to minimize the investment and operational costs of energy storage. The lower level is the intra-day operation optimization for prosumers, which reduces electricity costs through peer-to-peer (P2P) transactions among prosumers and the coordinated dispatch of SES. Meanwhile, an improved Nash bargaining method is introduced to reasonably allocate the P2P transaction benefits among prosumers based on their contributions to the transaction process. The case study shows that the proposed model can reduce the SES configuration capacity by 46.3% and decrease the annual electricity costs of prosumers by 0.98% to 27.30% compared with traditional SES, and the renewable energy consumption rate has reached 100%. Through peak–valley electricity price arbitrage, the annual revenue of the SES operator increases by 71.1%, achieving a win–win situation for prosumers and SES. This article, by optimizing the storage configuration and trading mechanism to make energy storage more accessible to users, enhances the local consumption of renewable energy, reduces both users′ energy costs and the investment costs of energy storage, and thereby promotes a more sustainable, resilient, and equitable energy future.