Entropy coincidence conjecture for cluster algebras and periodic Laurent-property maps

Let ${\cal A}$ be a cluster algebra, or let $\varphi$ be a map with the Laurent property obtained from a cluster algebra with periodicity in the sense of the cited constructions. Let ${\cal E}$ denote algebraic entropy and ${\cal E}_M$ denote Mahler entropy. Entropy coincidence conjecture. For cluster algebras ${\cal A}$, and for maps $\varphi$ with the Laurent property obtained from cluster algebras with periodicity, the algebraic and Mahler entropies coincide:

$${\cal E}={\cal E}_M.$$

This would make Mahler entropy independent of the choice of seed, up to mutation equivalence, and identify it with degree-growth entropy in these settings; the source does not state that the claim has been resolved.