Person re-identification (Re-ID) systems in edgecloud continuum face critical trade-offs between latency sensitivity and energy efficiency due to the resource-constrained edge environment. This paper proposes Re-IDFaaS, a serverless ReID system that dynamically optimizes energy consumption and computational performance across the edge-cloud continuum. Leveraging serverless architectures, our system implements three key improvements: (1) An event-driven workflow triggered by motion detection, eliminating idle GPU resource consumption during inactive periods. (2) A hardware-aware dynamic scheduler that allocates tasks based on real-time energy states and container availability, achieving balanced resource utilization across heterogeneous nodes. (3) An adaptive batching mechanism that reduces cold-start frequency through latency-constrained request grouping while maintaining the efficiency of GPU memory. Experiments demonstrate a 23.3% improvement in edge node availability and 55% reduction in memory usage compared to existing methods. The system design provides practical insights for building AI services in hybrid computing environments requiring cross-framework compatibility and adaptive resource orchestration, achieving 53% higher throughput than traditional architectures. These innovations address the challenges of dynamic workload scheduling and runtime optimization in hardware-diverse scenarios, ensuring sustainable operation under bursty surveillance workloads.