The conjecture on coisotropic structures and shifted Lagrangian reduction

Let $f:X\rightarrow Y$ be a finitely presented morphism of affine derived $k$-schemes, with $Y$ of finite presentation. An $n$-shifted coisotropic structure on $f$ is related to a diagram involving $X$, its symplectic thickening $X^{\mathrm{symp}}$, $Y^{\mathrm{symp}}$, and the prestack $X//f$, with maps $\pi_X$, $\pi_Y$, $\pi_f$, and $\mathrm{red}$ as displayed in the source.

Coisotropic reduction conjecture. The space of $n$-shifted coisotropic structures on $f$ is equivalent to the space of such diagrams, where $\pi_Y$ is an $(n+1)$-shifted Lagrangian thickening, $\pi_f$ is an $(n+1)$-shifted Lagrangian morphism, $\pi_X$ is an $n$-shifted Lagrangian thickening, $\mathrm{red}$ is a thickening, and the two $n$-shifted symplectic structures on $X^{\mathrm{symp}}$ are identified, one induced by the Lagrangian structure on $\pi_X$ and the other by the Lagrangian intersection. The prestack $X//f$ is called the coisotropic reduction of $f$.

This is posed in the context of extending formal localization to shifted coisotropic structures and coisotropic reductions. The source presents it as a conjecture and gives no evidence that it has been resolved.