Bolza surface conjecture for extremal-length systoles in genus 2

Let $\mathcal{M}_2$ denote the moduli space of conformal classes of closed genus-$2$ surfaces. For a conformal class $X\in\mathcal{M}_2$, let $\operatorname{sys}_{\operatorname{EL}}(X)$ be the minimum extremal length of an essential simple closed curve on $X$. Bolza surface conjecture. The maximum of $\operatorname{sys}_{\operatorname{EL}}$ in genus $2$ is attained by the conformal class of the Bolza surface. The Bolza surface is known to realize the maximum of the hyperbolic systole in genus $2$ and also appears as a maximizer for other notions of systolic length; whether it maximizes the extremal-length systole remains open.