The remainder of this work is structured as follows: in Sec. II, we first present an open quantum system model for describing chemical reactions in an optical cavity, accounting for both solvent effects and cavity losses. Subsequently, we introduce the mixed quantum-classical approach, wherein molecular vibrational dynamics are treated quantum mechanically while cavity photonic dynamics are described classically. Moving on to Sec. III, we assess the significance of the quantum nature of the cavity radiation field in shaping the resonance peak structure observed in cavity-induced modifications of chemical reactivity. Lastly, in Sec. IV, we highlight the importance of our findings in advancing further theoretical exploration of polariton chemistry.