SplitFed Learning (SFL) combines federated learning and split learning to enable collaborative training across distributed edge devices; however, it faces significant challenges in heterogeneous environments with diverse computational and communication capabilities. This paper proposes \textit{SuperSFL}, a federated split learning framework that leverages a weight-sharing super-network to dynamically generate resource-aware client-specific subnetworks, effectively mitigating device heterogeneity. SuperSFL introduces Three-Phase Gradient Fusion (TPGF), an optimization mechanism that coordinates local updates, server-side computation, and gradient fusion to accelerate convergence. In addition, a fault-tolerant client-side classifier and collaborative client--server aggregation enable uninterrupted training under intermittent communication failures. Experimental results on CIFAR-10 and CIFAR-100 with up to 100 heterogeneous clients show that SuperSFL converges $2$--$5\times$ faster in terms of communication rounds than baseline SFL while achieving higher accuracy, resulting in up to $20\times$ lower total communication cost and $13\times$ shorter training time. SuperSFL also demonstrates improved energy efficiency compared to baseline methods, making it a practical solution for federated learning in heterogeneous edge environments.