Speech super-resolution (SR) reconstructs high-fidelity wideband speech from low-resolution inputs-a task that necessitates reconciling global harmonic coherence with local transient sharpness. While diffusion-based generative models yield impressive fidelity, their practical deployment is often stymied by prohibitive computational demands. Conversely, efficient time-domain architectures lack the explicit frequency representations essential for capturing long-range spectral dependencies and ensuring precise harmonic alignment. We introduce STSR, a unified end-to-end framework formulated in the MDCT domain to circumvent these limitations. STSR employs a Spectral-Contextual Attention mechanism that harnesses hierarchical windowing to adaptively aggregate non-local spectral context, enabling consistent harmonic reconstruction up to 48 kHz. Concurrently, a sparse-aware regularization strategy is employed to mitigate the suppression of transient components inherent in compressed spectral representations. STSR consistently outperforms state-of-the-art baselines in both perceptual fidelity and zero-shot generalization, providing a robust, real-time paradigm for high-quality speech restoration.