This research presents an end-to-end integration system that uses an automated methodology to diagnose any type of thoracic disease and manage patients using chest radiography. The main obstacles in medical imaging related to patient data privacy, early-stage diagnosis, and care delivery delays will be addressed via federated vision transformers, longitudinal sequence analysis, and geospatial optimization of care dimensions. Three pillars support the suggested architecture: (1) a vision transformer based on federated learning that incorporates maximum-posteriori estimation and feedback training (MPEFT) compression with ε = 1.28 differential privacy, allowing for safe and secure training of federated multi-institutional models; (2) a temporal analysis engine that tracks the disease's progression over a series of X-ray images using time-aware attention mechanisms; (3) a care pathway optimizer that dynamically recommends suitable treatment facilities by taking into account 12 clinical and logistical parameters, including insurance coverage and bed availability. Experiments on different institutional datasets demonstrate a substantial improvement over the centralized CNN techniques, with diagnosis accuracy of 97.1%, 0.96 F1-score, and 23 ms inference latency. Additionally, the technology guaranteed 92% compliance for automatic referrals from insurers and reduced the diagnosis-to-treatment time by 83%. These findings demonstrate the promise of fully federated AI with privacy protection, transforming diagnosis by providing timely, equitable, and distributed healthcare in resource-constrained contexts.