  We present an ultraviolet-to-infrared search for the electromagnetic (EM)
counterpart to GW190425, the second-ever binary neutron star (BNS) merger
discovered by the LIGO-Virgo-KAGRA Collaboration (LVK). GW190425 was more
distant and had a larger localization area than GW170817, therefore we use a
new tool teglon to redistribute the GW190425 localization probability in the
context of galaxy catalogs within the final localization volume. We derive a
90th percentile area of 6,688 deg$^{2}$, a $\sim$1.5$\times$ improvement
relative to the LIGO/Virgo map, and show how teglon provides an order of
magnitude boost to the search efficiency of small ($\leq$1 deg$^{2}$)
field-of-view instruments. We combine our data with all publicly reported
imaging data, covering 9,078.59 deg$^2$ of unique area and 48.13% of the
LIGO/Virgo-assigned localization probability, to calculate the most
comprehensive kilonova, short gamma-ray burst (sGRB) afterglow, and
model-independent constraints on the EM emission from a hypothetical
counterpart to GW190425 to date under the assumption that no counterpart was
found in these data. If the counterpart were similar to AT 2017gfo, there was a
28.4% chance that it would have been detected in the combined dataset. We are
relatively insensitive to an on-axis sGRB, and rule out a generic transient
with a similar peak luminosity and decline rate as AT 2017gfo to 30%
confidence. Finally, across our new imaging and all publicly-reported data, we
find 28 candidate optical counterparts that we cannot rule out as being
associated with GW190425, finding that 4 such counterparts discovered within
the localization volume and within 5 days of merger exhibit luminosities
consistent with a kilonova.
