Consistency of a continuum bound for cellular-Lindelöf spaces with a Gδ diagonal of rank 2

Determine whether it is consistent with ZFC that every cellular-Lindelöf topological space with a Gδ diagonal of rank 2 has cardinality at most the continuum.

Background

The authors reference prior results showing the consistency of the continuum bound under additional hypotheses (e.g., normality). Further partial answers have been obtained in the literature, yet the general consistency statement for cellular-Lindelöf spaces with a Gδ diagonal of rank 2 remains open.

This problem concerns a set-theoretic consistency question, asking whether ZFC allows the continuum bound uniformly for this class.