As a final remark, achieving a deeper and more robust understanding of the collective effect necessitates further efforts beyond the scope of the current work, aimed at reaching the experimental limit where a macroscopic number of molecules are collectively coupled to a collection of cavity modes. In our future endeavors, we plan to employ the HEOM method in conjunction with a more advanced tensor network state approach. This approach will enable us to incrementally increase the number of the molecules inside the cavity from two to dozens, and to assess which approximations can be safely invoked at each stage, before attempting to bridge the gap to the experimental regime.