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Osteoporosis is a skeletal disease typically diagnosed using dual-energy X-ray absorptiometry (DXA), which quantifies areal bone mineral density but overlooks bone microarchitecture and surrounding soft tissues. High-resolution peripheral quantitative computed tomography (HR-pQCT) enables three-dimensional microstructural imaging with minimal radiation. However, current analysis pipelines largely focus on mineralized bone compartments, leaving much of the acquired image data underutilized. We introduce a fully automated framework for binary osteoporosis classification using radiomics features extracted from anatomically segmented HR-pQCT images. To our knowledge, this work is the first to leverage a transformer-based segmentation architecture, i.e., the SegFormer, for fully automated multi-region HR-pQCT analysis. The SegFormer model simultaneously delineated the cortical and trabecular bone of the tibia and fibula along with surrounding soft tissues and achieved a mean F1 score of 95.36%. Soft tissues were further subdivided into skin, myotendinous, and adipose regions through post-processing. From each region, 939 radiomic features were extracted and dimensionally reduced to train six machine learning classifiers on an independent dataset comprising 20,496 images from 122 HR-pQCT scans. The best image level performance was achieved using myotendinous tissue features, yielding an accuracy of 80.08% and an area under the receiver operating characteristic curve (AUROC) of 0.85, outperforming bone-based models. At the patient level, replacing standard biological, DXA, and HR-pQCT parameters with soft tissue radiomics improved AUROC from 0.792 to 0.875. These findings demonstrate that automated, multi-region HR-pQCT segmentation enables the extraction of clinically informative signals beyond bone alone, highlighting the importance of integrated tissue assessment for osteoporosis detection.