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With the increasing demand for wireless connectivity, ensuring the efficient coexistence of multiple radio access technologies in shared unlicensed spectrum has become an important issue. This paper focuses on optimizing Medium Access Control (MAC) parameters to enhance the coexistence of 5G New Radio in Unlicensed Spectrum (NR-U) and Wi-Fi networks operating in unlicensed spectrum with multiple priority classes of traffic that may have varying quality-of-service (QoS) requirements. In this context, we tackle the coexistence parameter management problem by introducing a QoS-aware State-Augmented Learnable (QaSAL) framework, designed to improve network performance under various traffic conditions. Our approach augments the state representation with constraint information, enabling dynamic policy adjustments to enforce QoS requirements effectively. Simulation results validate the effectiveness of QaSAL in managing NR-U and Wi-Fi coexistence, demonstrating improved channel access fairness while satisfying a latency constraint for high-priority traffic.