Graph Neural Networks (GNNs), particularly In-teraction Networks (INs), have shown exceptional performance for jet tagging at the CERN High-Luminosity Large Hadron Collider (HL-LHC). However, their computational complexity and irregular memory access patterns pose significant challenges for deployment on FPGAs in hardware trigger systems, where strict latency and resource constraints apply. In this work, we propose JEDI-linear, a novel GNN architecture with linear computational complexity that eliminates explicit pairwise interactions by leveraging shared transformations and global aggregation. To further enhance hardware efficiency, we introduce fine-grained quantization-aware training with per-parameter bitwidth optimization and employ multiplier-free multiply-accumulate operations via distributed rithmetic. Evaluation results show that our FPGA-based JEDI-linear achieves 3.7 to 11.5 times lower latency, up to 150 times lower initiation interval, and up to 6.2 times lower LUT usage compared to state-of-the-art designs while also delivering higher model accuracy and eliminating the need for DSP blocks entirely. In contrast, state-of-the-art solutions consume over 8,700 DSPs. This is the first interaction-based GNN to achieve less than 60 ns latency and currently meets the requirements for use in the HL-LHC CMS Level-1 trigger system. This work advances the next-generation trigger systems by enabling accurate, scalable, and resource-efficient GNN inference in real-time environments. Our open-sourced templates will further support reproducibility and broader adoption across scientific applications.