The higher Morita conjecture for finite tensor categories

Let $\mathbf{Vec}$ denote the category of finite-dimensional vector spaces over a field $\mathbb K$. The object $\Sigma^2\mathbf{Vec}$ is the twofold delooping associated to vector spaces. Higher Morita conjecture. $\Sigma^2\mathbf{Vec}$ is equivalent to the $3$-category whose objects are separable finite tensor categories and whose $1$-morphisms are their separable bimodule categories. This is the expected description one categorical dimension above the established description of $\Sigma\mathbf{Vec}$ by finite-dimensional separable algebras and bimodules. The source explicitly notes that the details were not checked, so the assertion remains open.