  We study critical properties of the entanglement and charge-sharpening
measurement-induced phase transitions in a non-unitary quantum circuit evolving
with a U(1) conserved charge. Many critical properties appear distinct from the
generic non-conserving case and percolation; however, upon interpreting the
critical features as mixtures of both entanglement and charge-sharpening
transitions, many critical features are brought within range of the generic
case. Nonetheless, the multifractal properties of the entanglement transition
remain distinct from the generic case without any symmetry, indicating a unique
universality class due to the U(1) symmetry. We compute entanglement critical
exponents and correlation functions via various ancilla measures, use a
transfer matrix for multifractality, and compute correlators associated with
charge sharpening to explain these findings. Through these correlators, we also
find evidence consistent with the charge-sharpening transition being of the
Berezinskii-Kosterlitz-Thouless type (including the predicted "jump" in
stiffness), which simultaneously argues for a broad critical fan for this
transition. As a result, attempts to measure critical properties in this system
will see anomalously large exponents consistent with overlapping criticality.
