Schmutz Schaller's systole-length conjecture for hyperbolic surfaces

Let $\mathcal M_g$ denote the moduli space of closed hyperbolic surfaces of genus $g$, and let $\operatorname{sys}(S)$ be the systole length of $S$. Schmutz Schaller's systole-length conjecture. There exists a constant $A>0$ such that

$$\max_{S\in \mathcal M_g} \operatorname{sys}(S)\leq \frac{4}{3}\log g+A.$$

This conjecture asserts that the maximal systole length grows logarithmically with genus, with leading coefficient $4/3$, matching the conjectured optimal asymptotic for arithmetic surfaces. The source gives no resolution, so its status remains open.