Nakajima's equivariant cohomology conjecture for truncated shifted Yangians

Let $B_h(\mathbf R)$ be the $B$-algebra of the Rees algebra of $Y^\lambda_\mu(\mathbf R)$, with $\mathbf R$ treated as formal variables, and let $\mathcal M(\mathbf m,W)$ be the corresponding Nakajima quiver variety. The coefficient ring $\mathbb C[e_k(R_i),h]$ is identified with $H^*_{G_W\times\mathbb C^\times}(*)$. Nakajima's conjecture. There should be an isomorphism of $\mathbb C[e_k(R_i),h]\cong H^*_{G_W\times\mathbb C^\times}(*)$-algebras

$$B_h(\mathbf R)\cong H^*_{G_W\times\mathbb C^\times}(\mathcal M(\mathbf m,W)).$$

In particular, after specializing $\mathbf R$ to numerical values and setting $h=1/2$, one should have

$$B(Y^\lambda_\mu(\mathbf R))\cong H^*(\mathbf m,W,\mathbf R).$$

The paper explicitly states that this conjecture is not known to be provable at that point.