Efficient spectrum management is critical for 6G mobile communications to meet stringent latency and bandwidth requirements of emerging edge computing applications. However, current spectrum management approaches face two primary challenges: inefficient spectrum utilization due to competitive conflicts among edge devices, and privacy concerns when sharing sensitive channel state information across the network. In this work, inspired by federated learning’s capability for privacy preservation, we present FedSM (Federated Spectrum Management), a novel hierarchical framework that addresses these challenges through two integrated modules: coalition-based spectrum allocation using hedonic coalition game theory to partition devices into strategic groups to reduce competitive conflicts, and bandit-based spectrum sharing employing contextual multi-armed bandit algorithms for adaptive resource allocation within coalitions while preserving privacy. Comprehensive evaluation on both Komondor simulator-based prototype testing and real-world VR application deployments demonstrates FedSM’s superior performance, achieving 93.51% channel utilization compared to 68.92% for baseline approaches in simulation environments, and 78% versus 30% for local management in real-world testbeds, while maintaining reasonable latency of 248.68 ms in simulation and competitive delay performance in real-world scenarios, all with complete privacy preservation.