Relative Witt quotient conjecture for faithfully flat enriched finite tensor categories

Let $\mathcal{E}$ be a finite symmetric tensor category. Let $\mathrm{Mor}_2^{\mathrm{fin}}(\mathbf{Pr}_{\mathcal{E}})$ be the symmetric monoidal sub-4-category whose objects are faithfully flat $\mathcal{E}$-enriched finite braided tensor categories, whose 1-morphisms are $\mathcal{E}$-enriched finite central pre-tensor categories, and whose 2-morphisms are $\mathcal{E}$-enriched finite centered bimodule categories. The group $\pi_0(\mathrm{Mor}_2^{\mathrm{fin}}(\mathbf{Pr}_{\mathcal{E}})^{\times})$ is the relative Witt quotient conjecture: it is isomorphic to the quotient of the monoid of $\mathcal{E}$-non-degenerate finite braided tensor categories by the submonoid of relative Drinfeld centers of faithfully flat $\mathcal{E}$-enriched finite tensor categories. This proposes a finite, non-separable generalization of relative Witt groups and gives an alternative to classifying all finite braided tensor categories; the source provides no evidence that the conjecture has been resolved.