The rapid proliferation of Internet of Things (IoT) devices and the transition to distributed computing environments necessitate advanced intrusion detection systems (IDS) to safeguard the new paradigm known as Cloud-Edge-IoT (CEI) continuum. In this paper, we introduce a novel approach called SURFS, integrating Hierarchical Federated Learning (HFL) with Spiking Neural Networks (SNN) to propose a robust, sustainable, and energy-efficient IDS for this continuum. HFL, with its hierarchical learning strategy, keeps data where they are generated, thus preserving user privacy and reducing communication overhead through its combination of decentralized and centralized architecture. On the other hand, SNN, inspired by human neural mechanisms, offers significant computational efficiency. Our proposed IDS combines these strengths, facilitating localized and energy-efficient detection at the edge and IoT layers while enabling global model aggregation and updates at the cloud layer. Through extensive experiments using one of the most recent datasets (Edge-IIoTset), we demonstrate that our approach not only detects attacks with high accuracy but also substantially reduces energy consumption across the continuum. The SURFS model presents a slightly superior performance in classification accuracy, outstripping the FL+SNN and non-FL models by margins of 0.5% and 1.21%; however, with a much faster convergence time (3× and 17× respectively). In terms of sustainability, it achieves a remarkable reduction in communication overhead 99% lower than FL+SNN and 97% lower than non-FL. Additionally, it showcases significant improvements in computational cost, being 62% more efficient than FL+SNN and 94% more efficient than the non-FL model.