In the era of crowd delivery vehicle routing and traffic management in smart cities, a complex challenge appears indistinctly, affecting both developed and developing nations worldwide. This challenging problem involves optimizing multi-depot routes while addressing various hurdles: minimizing travel time, distance, fuel consumption, and carbon emissions, all while navigating dynamic traffic congestion across diverse pathways. Existing approaches often focus on isolated aspects like shortest paths, carbon emissions, or traffic prediction, leaving the comprehensive multi-depot traffic management problem unaddressed. In response, this research work proposes an Intelligent Multi-Depot Vehicle Routing and Management (IM-VRM) model which provides a comprehensive and holistic solution. It employs a Graph Neural Network (GNN) learning-based routing with a greedy optimization to establish initial optimal pathways for multi-depot journeys. Subsequently, the IM-VRM model integrates traffic congestion prediction with green parameter computation, engaging the Dijkstra algorithm to select the most admissible routes. This consecutive steps-based travel route guidance process optimizes routing for heterogeneous vehicles, including both heavy-duty and light-duty types. It accounts for load-dependent fuel consumption, velocity, and carbon emissions. By doing so, it simplifies the complexities of multi-depot traffic routing and management. The proposed model has been rigorously evaluated using a real-world multi-depot traffic dataset, demonstrating its practical viability. Notably, IM-VRM model achieves a remarkable improvement in fuel savings, reduced carbon emissions, and shorter travel time outperforming previous state-of-the-art methods in both efficiency and precision.