Lagrangianity conjecture for singular support on rigid analytic varieties

Let $X$ be a smooth rigid analytic variety, and let $\mathcal{F}\in D^{(b)}_{zc}(X)$. The singular support $SS(\mathcal{F})$ is a closed subset of the cotangent bundle $T^*X$.

Lagrangianity conjecture. $SS(\mathcal{F})$ is an analytic Lagrangian subspace of $T^*X$, meaning that it is an analytic closed subset and is Lagrangian on its regular locus. In particular, if $X$ is connected, every irreducible component of $SS(\mathcal{F})$ has dimension $\dim(X)$.

The source says this conjecture is true on smooth surfaces, after possibly removing a discrete set of classical points, assuming $\Lambda=\mathbf{F}_{\ell^r}$. Its general validity remains open.