Shumyatsky's nilpotency conjecture for multilinear commutator values

Let $w$ be a multilinear commutator word and let $G$ be a finite group in which $|ab|=|a||b|$ whenever the $w$-values $a,b$ have coprime orders. Shumyatsky's conjecture. Then $w(G)$ is nilpotent. This conjecture asks whether the order-multiplication condition on coprime-order $w$-values forces the verbal subgroup $w(G)$ to be nilpotent. It is known for certain families of commutator words, including the simple commutator words described in the preceding result, but remains open for general multilinear commutator words.