A novel deep hybrid Residual-SwinCA-Net segmentation framework is proposed in the study for addressing such challenges by extracting locally correlated and robust features, incorporating residual CNN modules. Furthermore, for learning global dependencies, Swin Transformer blocks are customized using internal residual pathways, which reinforce gradient stability, refine local patterns, and facilitate global feature fusion. Formerly, for enhancing tissue continuity, ultrasound noise suppressions, and accentuating fine structural transitions Laplacian-of-Gaussian regional operator is applied, and for maintaining the morphological integrity of malignant lesion contours, a boundary-oriented operator has been incorporated. Subsequently, a contraction strategy was applied stage-wise by progressively reducing features-map progressively for capturing scale invariance and enhancing the robustness of structural variability. In addition, each decoder level prior augmentation integrates a new Multi-Scale Channel Attention and Squeezing (MSCAS) module. The MSCAS selectively emphasizes encoder salient maps, retains discriminative global context, and complementary local structures with minimal computational cost while suppressing redundant activations. Finally, the Pixel-Attention module encodes class-relevant spatial cues by adaptively weighing malignant lesion pixels while suppressing background interference. The Residual-SwinCA-Net and existing CNNs/ViTs techniques have been implemented on the publicly available BUSI dataset. The proposed Residual-SwinCA-Net framework outperformed and achieved 99.29% mean accuracy, 98.74% IoU, and 0.9041 Dice for breast lesion segmentation. The proposed Residual-SwinCA-Net framework improves the BUSI lesion diagnostic performance and strengthens timely clinical decision-making.