The Hikita conjecture for symplectically dual resolutions

Let $X$ and $X^!$ be symplectically dual, and let $Y$ be the affinization of $X$. Let $Y^T$ denote the scheme-theoretic fixed locus of $Y$ under the $T$-action, with grading induced by the scaling $\mathbb{G}_m$-action. Hikita conjecture. There exists an isomorphism of graded algebras

$$\mathcal{O}(Y^T) \cong H^*(X^!;k).$$

The conjecture identifies the cohomology of the dual resolution with the coordinate ring of the fixed locus; it is the classical precursor of the Hikita--Nakajima and quantum Hikita conjectures. The source gives no resolution status.