We use HDGAS hydrodynamic simulations to study the impact of active galactic nucleus (AGN) feedback on the conversion of atomic-gas to molecular-gas within the circumnuclear-disc (CND) of a typical AGN-dominated galaxy. The comparison of CI, CII, and CO line intensities and their ratios in the HDGAS post-processing radiative-transfer analysis reveals the complex interplay between AGN-activity, cold molecular gas properties, and the physical processes governing the evolution of star-formation in galaxies. Our results demonstrate that the CI/CO intensity ratio serves as a reliable indicator of the atomic-to-molecular gas transition. We present the probability distribution function (PDF) and abundance trends of various metal species related to molecular H$2$ gas, highlighting differences in clumpiness and intensity maps between AGN feedback and NoAGN models. The profile of the integrated intensity (moment-0) maps shows that the AGN-feedback model exhibits a lower CI/CO intensity ratio in the vicinity of the supermassive black hole (< 50 pc), indicating a smaller atomic-gas abundance and the presence of positive AGN-feedback. Our simulations have successfully predicted the presence of faint-CO emissions extending to larger radii from the galactic center. We also explore the relationships between CII/CO and CI/CII intensity ratios, as well as the ratios versus CO intensity, which provides insights into the "CO-dark" issues. One notable feature in the later time-scale of the AGN model is the presence of a "CO-dark" region, where the intensity of CO emission ($\rm I_{CO}$) is depleted relative to the H$_2$ column density ($N_{\rm H_2}$) compared to the NoAGN model.