, and a Γ pt value yielding the cavity lifetime of τ c = 2J pt (ω c ) ω c (1-e -β ωc) = 200fs. The baths are maintained at room temperature T = 300K, and each is simulated with four effective dissipative bosons per bath. The maximum occupation number n α p per effective boson spans up to 10. For simplicity, we assume that the phonon bath exclusively interacts with the molecular vibration, characterized by s ph (x m ,x c ) = x m , while the photon bath couples solely to the cavity mode, represented by s pt (x m ,x c ) = x c . Additionally, we employ a maximal bond dimension D max = 30 and a time step ∆t = 0.5fs.