Surface electromyography (sEMG)-based gesture recognition is the core technology for neuroprosthetic control, yet its practical application is severely hindered by the non-stationarity and inter-session variability of sEMG signals, as well as the catastrophic forgetting (CF) problem in incremental learning and the resource constraints of embedded devices. Conventional sEMG classification models either lack effective cross-session adaptation capabilities or fail to balance the latency-accuracy-memory trade-off in embedded deployment, while existing incremental learning strategies lack systematic optimization for high-dimensional temporal sEMG signals and engineering verification on actual hardware platforms. To address these challenges, this study proposes an end-to-end on-device continual learning framework for sEMG-based neuroprosthetic control based on the TCNformer hybrid network architecture, which fuses Temporal Convolutional Network (TCN) and Transformer.