Federated learning (FL) enables collaborative intrusion detection without raw data exchange, but conventional FL incurs high communication overhead from full-precision gradient transmission and remains vulnerable to gradient inference attacks. This paper presents EdgeDetect, a communication-efficient and privacy-aware federated IDS for bandwidth-constrained 6G-IoT environments. EdgeDetect introduces gradient smartification, a median-based statistical binarization that compresses local updates to {+1,-1} representations, reducing uplink payload by 32times while preserving convergence. We further integrate Paillier homomorphic encryption over binarized gradients, protecting against honest-but-curious servers without exposing individual updates. Experiments on CIC-IDS2017 (2.8M flows, 7 attack classes) demonstrate 98.0% multi-class accuracy and 97.9% macro F1-score, matching centralized baselines, while reducing per-round communication from 450~MB to 14~MB (96.9% reduction). Raspberry Pi-4 deployment confirms edge feasibility: 4.2~MB memory, 0.8~ms latency, and 12~mJ per inference with <0.5% accuracy loss. Under 5% poisoning attacks and severe imbalance, EdgeDetect maintains 87% accuracy and 0.95 minority class F1 (p<0.001), establishing a practical accuracy, communication, and privacy tradeoff for next-generation edge intrusion detection.