Berman's genuine equivariant presentability conjecture

Let $G$ be a finite group, let $\text{Burn}_G^{(\infty,2)}$ be the genuine equivariant Burnside $(\infty,2)$-category, and let $\text{Pr}^{\text{L}}$ be the $\infty$-category of presentable $\infty$-categories. A genuine $G$-equivariant cocartesian monoidal $\infty$-category consists of the corresponding product-preserving functor to $\text{Cat}$. Genuine equivariant presentability conjecture. A genuine $G$-equivariant presentable $\infty$-category is a product-preserving functor

$$\text{Burn}_G^{(\infty,2)}\rightarrow\text{Pr}^{\text{L}};$$

that is, a genuine $G$-equivariant cocartesian monoidal $\infty$-category $\mathcal{C}$ such that each $\infty$-category $\mathcal{C}_H$ for $H<G$ is presentable, and each transfer and restriction has a right adjoint. The conjecture is offered as a proposed notion of equivariant presentable $\infty$-category; no proof or resolution is given.