The Kapranov potential conjecture for smooth symplectic schemes

Let $(X,\omega)$ be a smooth symplectic scheme. Kapranov's cyclic $L_\infty$ structure on $\mathrm{T}_X[-1]$ has a potential in $\Gamma(X,\widehat{\operatorname{Sym}}^{\geq 3}(\mathrm{T}_X))$ of cohomological degree $1$. Kapranov's potential conjecture. The $(-1)$-shifted Poisson structure on $X$ obtained as the image of $\omega$ under the forgetful map

$$\operatorname{Pois}(X,0)\longrightarrow \operatorname{Pois}(X,-1)$$

gives the potential for this cyclic $L_\infty$ structure. The claim identifies the shifted Poisson structure naturally induced by the symplectic form with Kapranov's potential; the accompanying discussion notes that its underlying bivector is trivial because the diagonal is Lagrangian with split normal bundle.