  We present updated constraints on the cosmological 3D power spectrum of
carbon monoxide CO(1-0) emission in the redshift range $2.4$-$3.4$. The
constraints are derived from the two first seasons of Carbon monOxide Mapping
Array Project (COMAP) Pathfinder line-intensity mapping observations aiming to
trace star-formation during the Epoch of Galaxy Assembly. These results improve
on the previous Early Science (ES) results through both increased data volume
and improved data processing methodology. On the methodological side, we now
perform cross-correlations between groups of detectors (''feed-groups''), as
opposed to cross-correlations between single feeds, and this new feed-group
pseudo power spectrum (FGPXS) is constructed to be more robust against
systematic effects. In terms of data volume, the effective mapping speed is
significantly increased due to an improved observational strategy as well as
better data selection methodology. The updated spherically- and field-averaged
FGPXS, $\tilde{C}(k)$, is consistent with zero, at a probability-to-exceed of
around $34\,\%$, with an excess of $2.7\,\sigma$ in the most sensitive bin. Our
power spectrum estimate is about an order of magnitude more sensitive in our
six deepest bins across ${0.09\,\mathrm{Mpc}^{-1} < k <
0.73\,\mathrm{Mpc}^{-1}}$, as compared to the feed-feed pseudo power spectrum
(FPXS) of COMAP ES. Each of these bins individually constrains the CO power
spectrum to ${kP_\mathrm{CO}(k)< 2400-4900\,\mathrm{\mu K^2 Mpc^{2}}}$ at
$95\,\%$ confidence. To monitor potential contamination from residual
systematic effects, we analyze a set of 312 difference-map null tests and find
that these are consistent with the instrumental noise prediction. In sum, these
results provide the strongest direct constraints on the cosmological 3D CO(1-0)
power spectrum published to date.
