Compatible correspondence conjecture for nondegenerate shifted coisotropic correspondences

Let $\mathrm{CompCorr}_{n}^{s,\operatorname{nd}}$ be the $(\infty,n)$-category of nondegenerate $s$-shifted compatible coisotropic correspondences, let $\mathrm{CoisCorr}_{n}^{s,\operatorname{nd}}$ be the corresponding category of nondegenerate coisotropic correspondences, and let $\mathrm{IsotCorr}_{n}^{s}$ and $\mathrm{Lag}_{n}^{s}$ denote the categories of isotropic and Lagrangian correspondences. Compatible correspondence conjecture. (1) The projection

$$\mathrm{CompCorr}_{n}^{s,\operatorname{nd}}\longrightarrow \mathrm{CoisCorr}_{n}^{s,\operatorname{nd}}$$

is an equivalence. (2) There is a symmetric monoidal functor

$$\mathrm{CompCorr}_{n}^{s,\operatorname{nd}}\longrightarrow \mathrm{IsotCorr}_{n}^{s}.$$

(3) This functor restricts to an equivalence

$$\mathrm{CompCorr}_{n}^{s,\operatorname{nd}}\longrightarrow \mathrm{Lag}_{n}^{s}.$$

These assertions would identify nondegenerate compatible coisotropic correspondences with ordinary nondegenerate coisotropic correspondences and relate them to isotropic and Lagrangian correspondences. The given text supplies no proof or resolution.