Semisimplicity conjecture for negligible quotients of supergroup homotopy categories

Let $G$ be a basic classical algebraic supergroup and let $H$ be a subgroup satisfying $G_0\subset H\subset G$. Put $\mathcal T=\operatorname{Rep}_k(G)$, let $Ho\mathcal T$ be its homotopy category, and let $\mathcal N$ be the monoidal ideal of negligible morphisms in $Ho\mathcal T$. Semisimplicity conjecture. The quotient

$$Ho\mathcal T/\mathcal N$$

is the semisimple representation category of an affine supergroup scheme. The quotient is intended to remove negligible morphisms and produce a semisimple tensor category associated with the supergroup representation theory. The source gives no resolution of this assertion; it appears after the hom-finiteness discussion and a special case of that discussion is proved for $(P(m|n)^+,GL(m|n))$.