In close proximity to quantum emitters (QEs), plasmonic nanoparticles (NPs) facilitate energy exchange with the QEs, which is known as plasmon–exciton coupling. The strong coupling regime, associated with Rabi splitting, is crucial for advanced nanophotonic devices, including solar cells, single-photon nonlinear optics, and nanolasers. Recently, high refractive index semiconductor NPs (typically Si NPs) have emerged for designing strongly coupled systems. However, their large mode volumes of magnetic Mie resonances have limited their success in achieving strong coupling. This study investigates the plasmon–exciton coupling between an Ag–Si core–shell and a monolayer QE of WS₂ (Ag–Si–WS₂ system) in air and water environments. Here, we compare the coupling dynamics of the hybrid Ag–Si–WS₂ system to that of the Si–WS₂ system as a benchmarking system. Employing Mie’s theory of core–shell scattering, in conjunction with Maxwell–Garnett effective medium theory, we analyze the optical responses of both configurations. Then, we calculate the Rabi splitting frequency for each system to identify the coupling regime. Our results suggest that the Ag–Si–WS₂ system can achieve a deep-strong coupling regime when the Ag core radius is less than 30 nm, with enhanced coupling strength in water compared to air. Conversely, the Si–WS₂ system does not achieve strong coupling in either medium. The hybrid modes in Ag–Si–WS₂ demonstrate remarkable symmetrical spectral characteristics compared to the asymmetric spectral line shape observed in the Si–WS₂ system. The findings suggest avenues for utilizing the plasmon–exciton strong coupling in the Ag–Si–WS₂ system to enhance optoelectronic and quantum electronic devices.