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The Carbon monOxide Mapping Array Project (COMAP) Pathfinder survey continues to demonstrate the feasibility of line-intensity mapping using high-redshift carbon monoxide (CO) line emission traced at cosmological scales. The latest COMAP Pathfinder power spectrum analysis is based on observations through the end of Season 2, covering the first three years of Pathfinder operations. We use our latest constraints on the CO(1-0) line-intensity power spectrum at to update corresponding constraints on the cosmological clustering of CO line emission and thus the cosmic molecular gas content at a key epoch of galaxy assembly. We first mirror the COMAP Early Science interpretation, considering how Season 2 results translate to limits on the shot noise power of CO fluctuations and the bias of CO emission as a tracer of the underlying dark matter distribution. The COMAP Season 2 results place the most stringent limits on the CO tracer bias to date, at K. These limits narrow the model space significantly compared to previous CO line-intensity mapping results while maintaining consistency with small-volume interferometric surveys of resolved line candidates. The results also express a weak preference for CO emission models used to guide fiducial forecasts from COMAP Early Science, including our data-driven priors. We also consider directly constraining a model of the halo-CO connection, and show qualitative hints of capturing the total contribution of faint CO emitters through the improved sensitivity of COMAP data. With continued observations and matching improvements in analysis, the COMAP Pathfinder remains on track …