This paper tackles decentralized continuous task allocation in heterogeneous multi-agent systems. We present a novel framework HIPPO-MAT that integrates graph neural networks (GNN) employing a GraphSAGE architecture to compute independent embeddings on each agent with an Independent Proximal Policy Optimization (IPPO) approach for multi-agent deep reinforcement learning. In our system, unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) share aggregated observation data via communication channels while independently processing these inputs to generate enriched state embeddings. This design enables dynamic, cost-optimal, conflict-aware task allocation in a 3D grid environment without the need for centralized coordination. A modified A* path planner is incorporated for efficient routing and collision avoidance. Simulation experiments demonstrate scalability with up to 30 agents and preliminary real-world validation on JetBot ROS AI Robots, each running its model on a Jetson Nano and communicating through an ESP-NOW protocol using ESP32-S3, which confirms the practical viability of the approach that incorporates simultaneous localization and mapping (SLAM). Experimental results revealed that our method achieves a high 92.5% conflict-free success rate, with only a 16.49% performance gap compared to the centralized Hungarian method, while outperforming the heuristic decentralized baseline based on greedy approach. Additionally, the framework exhibits scalability with up to 30 agents with allocation processing of 0.32 simulation step time and robustness in responding to dynamically generated tasks.