To address the high-dimensional search space, frequent conflicts, and limited planning efficiency in multi-arm collaborative path planning in complex constrained environments, a multi-arm collaborative planning method integrating graph neural networks with conflict-based search (GNN-CBS) is proposed. First, a key-region-biased sampling strategy is introduced during random geometric graph construction. Gaussian mixture models are used to probabilistically model constrained passage regions between obstacles and inter-arm interaction conflict regions, thereby improving graph connectivity while preserving sampling completeness. Second, a low-level neural planner trained with a composite loss function is designed to promote consistency between local decisions and global path structures, reducing redundant search and collision-checking costs. In addition, a high-level coordination mechanism based on conflict-based search, together with spatiotemporal constraint masking, adjusts only locally affected search spaces when conflicts arise, thereby effectively decoupling geometric planning from spatiotemporal coordination. Simulation and real-robot experiments demonstrate that the proposed method maintains a high task success rate in complex multi-arm scenarios and outperforms multiple conventional planning methods and learning-based baselines in planning time and computational efficiency, demonstrating its stability and scalability in large-scale collaborative tasks.