  We investigate the impact of nonreciprocity on universality and critical
phenomena in open quantum interacting many-body systems. Nonreciprocal open
quantum systems often have an exotic spectral sensitivity to boundary
conditions, known as the Liouvillian skin effect (LSE). By considering an open
quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a
universal scaling regime that is not affected by the presence of the LSE. We
resolve the critical exponents, which differ from those of free fermions, via
tensor network methods and demonstrate that observables exhibit a universal
scaling collapse, irrespective of the reciprocity. We find that the LSE only
becomes relevant when a healing length scale $\xi_{\rm heal}$ at the system's
edge (which is different to the localization length of the eigenstate of the
Liouvillian) exceeds the system size, allowing edge properties to dominate the
physics. We expect this result to be a generic feature of nonreciprocal models
in the vicinity of a critical point. The driven-dissipative quantum criticality
we observe has no classical analogue and stems from the existence of multiple
dark states.
