Aharoni–Zerbib's generalization of Tuza's conjecture

Let $H$ be a $3$-uniform hypergraph. For a positive integer $m$, let $\nu^{(m)}(H)$ be the maximum size of a collection of edges no two of which share $m$ or more vertices, and let $\tau^{(m)}(H)$ be the minimum size of a collection of $m$-sets such that every edge of $H$ contains one of them.

Aharoni–Zerbib's generalization of Tuza's conjecture. Every $3$-uniform hypergraph satisfies

$$\tau^{(2)}(H)\leq 2\nu^{(2)}(H).$$

This extends the triangle-hypergraph formulation of Tuza's conjecture to all $3$-uniform hypergraphs. The source gives no resolution status.