RCD topological stability conjecture under noncollapsed three-dimensional convergence

Let $(X_i,\mathsf{d}_i,\mathscr{H}^3)$ be $\operatorname{RCD}(-2,3)$ spaces. Assume that

$$(X_i,\mathsf{d}_i)\xrightarrow{\mathrm{GH}}(X,\mathsf{d})\, \quad \text{as $i\to\infty$}\,,$$

without collapse, for some compact $\operatorname{RCD}(-2,3)$ space $(X,\mathsf{d},\mathscr{H}^3)$.

RCD stability conjecture. There exists $i_0\in\mathbb{N}$ such that $X_i$ is homeomorphic to $X$ for every $i\ge i_0$.

This would remove the manifold assumption from the three-dimensional stability theorem. The source presents it as a consequence that would follow if Mondino's orbifold conjecture held, and does not specify a resolution.