With the breakthrough developments in clean energy and energy storage technologies, shared hydrogen storage power stations (SHSPS) are becoming a new application model for energy storage systems. To meet the collaborative optimization needs of multiple stakeholders (including SHSPS and low-carbon building microgrid clusters), this study proposes a Stackelberg game-based multi-time scale capacity configuration framework for SHSPS, aiming to achieve efficient utilization of hydrogen-electric coupled systems. Specifically, the upper-level leader (SHSPS) conducts long-term capacity planning targeting operational economy while incorporating hydrogen’s seasonal characteristics, and the lower-level followers (low-carbon building microgrid clusters，LBMC) optimize short-term operations under cooling, heating, and electricity load constraints. By transforming the bi-level game model into a solvable bi-level optimization problem using KKT conditions, the method’s effectiveness is validated through a real-world case study in a Shanghai region. Results show the proposed approach overcomes the limitations of traditional configuration models in multi-timescale analysis. While ensuring optimal system power configuration, it maximizes bidirectional economic benefits for both SHSPS and LBMC operators and significantly improves the renewable energy accommodation rate.