Regularity bound for squarefree parts of symbolic powers of edge ideals

Let $G$ be a graph, let $I(G)$ denote its edge ideal, let $I(G)^{\{s\}}$ denote the squarefree part of its $s$-th symbolic power, and let ${\rm match}(G)$ denote the matching number of $G$. Squarefree symbolic-power regularity conjecture. For every integer $s$ such that $I(G)^{\{s\}}\neq 0$, one has

$${\rm reg}(I(G)^{\{s\}})\leq {\rm match}(G)+s.$$

This proposes that the matching-number upper bound known in the source for squarefree powers should also hold for squarefree parts of symbolic powers. The source presents this as a conjecture and supplies no evidence of resolution.