Under the “dual-carbon” target, geothermal energy has become an important direction for energy transition due to its characteristics of being clean and efficient, having abundant reserves, and being low-carbon and environmentally friendly. Aiming at the seepage–heat transfer evolution characteristics and well-pattern optimization of geothermal fields under multi-well production and reinjection conditions, this study takes the geothermal field in the Xiong'an high-speed railway area as the research object. A three-dimensional coupled seepage–heat transfer numerical model was constructed based on COMSOL Multiphysics, and parameter calibration was carried out by combining field monitoring data of production-well water temperature and groundwater level to ensure consistency between numerical results and actual operation conditions. On this basis, twenty additional geothermal wells were designed, including ten production wells and ten reinjection wells. By simulating three well-pattern schemes—linear, staggered, and triangular—the variations in production-well water level, temperature, and dynamic recoverable geothermal resources under different schemes were analyzed, and the influences of different schemes on reservoir stability and heat-exchange efficiency were systematically compared. The results show that the linear well pattern has a simple structure and is easy to implement; however, its thermal mobilization range is limited, the overall recoverable geothermal resources are the lowest, and boundary production wells are prone to forming localized groundwater drawdown cones. The staggered well pattern exhibits a more uniform distribution of production and reinjection, which can effectively suppress localized overexploitation, delay cold-water breakthrough, and maintain relatively high reservoir thermal stability, resulting in the most stable evolution of dynamic recoverable geothermal energy. The triangular well pattern shows the strongest thermal mobilization capacity and the highest recoverable geothermal resources during the early stage of operation, but the risk of cold-water intrusion increases in areas with high production-well density, leading to a tendency of localized thermal attenuation in the later stage of operation. On a 50-year timescale, the total recoverable geothermal resources of both the staggered and triangular well patterns are more than 1% higher than those of the linear well pattern. Among them, the staggered well pattern achieves the best balance between resource utilization efficiency and system stability and is recommended as the preferred well-pattern scheme for the efficient and sustainable development of the geothermal field in the study area. The research results can provide theoretical references for well-pattern optimization, development performance evaluation, and sustainable operation of multi-well production and reinjection systems in mid-to deep-depth hydrothermal geothermal fields under similar geological settings and operating conditions.