The integration of Reinforcement Learning (RL) into robotic-assisted surgery (RAS) holds significant promise for advancing surgical precision, adaptability, and autonomous decision-making. However, the development of robust RL models in clinical settings is hindered by key challenges, including stringent patient data privacy regulations, limited access to diverse surgical datasets, and high procedural variability. To address these limitations, this paper presents a Federated Deep Reinforcement Learning (FDRL) framework that enables decentralized training of RL models across multiple healthcare institutions without exposing sensitive patient information. A central innovation of the proposed framework is its dynamic policy adaptation mechanism, which allows surgical robots to select and tailor patient-specific policies in real-time, thereby ensuring personalized and Optimised interventions. To uphold rigorous privacy standards while facilitating collaborative learning, the FDRL framework incorporates secure aggregation, differential privacy, and homomorphic encryption techniques. Experimental results demonstrate a 60\% reduction in privacy leakage compared to conventional methods, with surgical precision maintained within a 1.5\% margin of a centralized baseline. This work establishes a foundational approach for adaptive, secure, and patient-centric AI-driven surgical robotics, offering a pathway toward clinical translation and scalable deployment across diverse healthcare environments.