Semikhatov–Tipunin's logarithmic Kazhdan–Lusztig correspondence conjecture

Let $V$ be one of the vertex algebras specified by the paper's extension pairs, let $A$ be the corresponding free field algebra, and let $\mathfrak{N}$ be the Nichols algebra generated by the screening operators inside $\mathrm{Rep}^{\mathrm{wt}}(A)$. Semikhatov–Tipunin's conjecture. (1) The category $\mathrm{Rep}^{\mathrm{wt}}(V)$ has a braided tensor structure in the sense of Huang–Lepowsky–Zhang and

$$\mathrm{Rep}^{\mathrm{wt}}(V)\simeq {}^{\mathfrak{N}}_{\mathfrak{N}}\mathcal{YD}(\mathrm{Rep}^{\mathrm{wt}}(A))$$

as braided tensor categories. (2) For $V=s\mathcal{M}_p(\mathfrak{sl}_{2|1})$,

$$\mathrm{Rep}^{\mathrm{wt}}(s\mathcal{M}_p(\mathfrak{sl}_{2|1}))\simeq\mathrm{Rep}^{\mathrm{wt}}(u_q^H(\mathfrak{sl}_{2|1})).$$

This is the proposed logarithmic Kazhdan–Lusztig correspondence for these vertex algebras; the source does not state that it has been resolved.