In the face of increasing climate-related challenges, sustainable urban energy networks must grapple with transmission congestion in deregulated power systems. This study introduces a novel statistical approach that synergizes two powerful methodologies for evaluating and managing urban energy networks: the integration of photovoltaic (PV) renewable energy sources and Gated Recurrent Unit (GRU)-based PV forecasting. By combining evolutionary optimization techniques with GRU forecasting, we aim to bolster the sustainability and reliability of urban energy networks while addressing climate change adaptation. In this study, we employ statistical methods, including generator sensitivity ratios and bus sensitivity ratios (BSR), to pinpoint optimal locations for PV power integration within urban networks. The Lion Optimization Algorithm (LOA), an evolutionary optimization method, is employed within a digital twin framework to optimize active power rescheduling values and congestion prices. The incorporation of GRU-based PV forecasting enhances the precision and resilience of our energy management approach. Through extensive simulations conducted on the New England 39-bus system, our findings reveal that the combination of the LOA method and GRU forecasting outperforms traditional optimization techniques such as the Ant Lion Optimizer (ALO) and Particle Swarm Optimization (PSO). This dual-optimization strategy leads to significantly reduced active power rescheduling values and congestion prices, underlining the potential of our statistical model to effectively manage congestion in transmission lines within sustainable urban energy networks. In the context of integrating renewable PV sources and adapting urban energy infrastructure to climate change impacts, the synergy of evolutionary optimization and GRU-based forecasting offers a robust pathway to enhance sustainability and reliability in urban energy networks.