Fully extended 3d mirror symmetry for sectorial symplectic resolutions

Let $(X\supset\mathbb L)$ and $(X^\vee\supset\mathbb L^\vee)$ be dual pairs of sectorial conical symplectic resolutions. Let $2\mathcal O_{\mathsf A}$ and $2\mathcal O_{\mathsf B}$, respectively $2\mathcal O_{\mathsf A}^\vee$ and $2\mathcal O_{\mathsf B}^\vee$, denote the associated A- and B-model 2-categories, each equipped with its canonical generator. Fully extended 3d mirror symmetry. There are equivalences of 2-categories

$$2\mathcal O_{\mathsf A}\simeq 2\mathcal O_{\mathsf B}^\vee,\qquad 2\mathcal O_{\mathsf B}\simeq 2\mathcal O_{\mathsf A}^\vee,$$

exchanging the canonical generators. This is proposed as a more fundamental statement about boundary conditions in dual theories, from which symplectic duality follows; it remains open in the source.