The design of orthogonal Multiple-Input Multiple-Output (MIMO) radar waveforms under spectral constraints is of great importance. Most existing methods focus on optimizing the Integrated Sidelobe Level (ISL), which often results in waveforms with high peak sidelobes. We observe that, by approximating the Peak Sidelobe Level (PSL) through a softmax-based differentiable formulation and leveraging the powerful nonlinear modeling ability of Deep Learning (DL), effective PSL optimization can be achieved. Moreover, we observe that the powerful nonlinear fitting capability of DL enables parallel training for multi-scenario waveform generation. Based on these insights, we propose the Cross-Attention Residual Enhancement Network (CARE-Net), a network that integrates residual structures with cross-attention mechanisms. The proposed CARE-Net is designed to jointly minimize range-PSL&ISL under spectral constraints and is flexible to support waveform design in various scenarios. Simulation results demonstrate that (1) the proposed method achieves approximately 2−5 dB peak sidelobe reduction compared to existing methods and (2) existing methods can only design a single waveform for a specific scenario, whereas our proposed method enables the simultaneous design of waveform sets for multiple scenarios.