  We extend a holomorphic projection argument of our earlier work to prove a
novel divisibility result for non-holomorphic congruences of Hurwitz class
numbers. This result allows us to establish Ramanujan-type congruences for
Hurwitz class numbers on square classes, where the holomorphic case parallels
previous work by Radu on partition congruences. We offer two applications. The
first application demonstrates common divisibility features of Ramanujan-type
congruences for Hurwitz class numbers. The second application provides a
dichotomy between congruences for class numbers of imaginary quadratic fields
and Ramanujan-type congruences for Hurwitz class numbers.
