The gradual replacement of conventional-fuel vehicles by electric vehicles (EVs) in recent years provides a growing incentive for the collaborative optimization of power distribution networks (PDNs) and urban transportation networks (UTNs). However, the implementation of a centralized optimization model for PDNs and UTNs is currently unrealistic due to the requirement for establishing information privacy barriers between the two independently operated networks. The present work proposes a predict-then-optimize (PTO) framework that combines Spatiotemporal Graph Attention Network (STGAT) with enhanced queueing theory to achieve accurate prediction of EV charging demands. Building upon this, it efficiently coordinates optimization between the PDN and UTN, while preserving the information privacy of both independently operated networks. Specifically, the proposed STGAT model predicts vehicle flow by simultaneously exploiting the dynamic temporal and spatial dependencies in the historical traffic data of the target UTN. It then converts the predicted flow into spatiotemporal EV charging demands using an enhanced queuing model that considers the service capacity constraints of charging stations (CSs) and the behavior of EV users. Subsequently, the predicted EV charging demands are integrated into a multi-period PDN scheduling model. The results of numerical computations based on an IEEE 33-bus PDN and real-world traffic flow datasets demonstrate that the scheduling results provided by the proposed approach differ by only 0.5% compared to results obtained when applying actual EV charging demands.