The 2-categorical universal property of the optic construction

Let $\mathbf{SymmMonCat}_\mathrm{homcore}$ be the sub-2-category of symmetric monoidal categories whose 2-morphisms are natural isomorphisms, and let $\mathbf{Tele}$ be the 2-category of teleological categories, functors, and teleological natural isomorphisms. Write $\mathbf{Optic}$ for the optic construction and $(-)_d$ for the underlying dualisable-morphisms functor.

Optic biadjunction conjecture. The functor

$$\mathbf{Optic}: \mathbf{SymmMonCat}_\mathrm{homcore} \to \mathbf{Tele}$$

is left biadjoint to

$$(-)_d: \mathbf{Tele} \to \mathbf{SymmMonCat}_\mathrm{homcore}.$$

The preceding strict universal property establishes the analogous ordinary adjunction for strict monoidal categories. This conjectural extension would provide the corresponding 2-categorical universal property for non-strict monoidal categories, restricted to natural isomorphisms.