Universal formality conjecture for connected subgraph arrangements

Let $G$ be a connected graph, and let ${\mathscr A}_G$ denote its connected subgraph arrangement. For an arrangement ${\mathscr A}$, $k$-formality is the hierarchy of formality properties defined for $1\leq k\leq \operatorname{rk}({\mathscr A})$. Universal formality conjecture. Any ${\mathscr A}_G$ is $k$-formal for any $k$. This is motivated by the fact that connected subgraph arrangements are formal, and that the claim is already known when the rank is at most $4$ or when the arrangement is free; computational evidence suggests it more generally, but the universal assertion remains open.