I don't have enough reputation to comment so I will post it as an answer. Some classification of symplectic resolutions was done by Namikawa (https://arxiv.org/abs/1305.1698). As observed in https://arxiv.org/pdf/1611.08340.pdf, given a singular variety $Y$ over a field of char 0 and provided there exists at least one symplectic resolution $\pi: X \rightarrow Y,$ the vector space $V_{\mathbb{R}}=\operatorname{Pic}(X) \otimes_{\mathbb{Z}} \mathbb{R}$ can be partitioned into a union of rational cones, and there is an action of a finite group $W$ on $V_{\mathbb{R}}$ that maps cones to cones. The set of symplectic resolutions $\pi: X \rightarrow Y$ is then identified with the set of cones modulo the action of $W$.

I don't have enough reputation to comment so I will post it as an answer. Some classification of symplectic resolutions was done by Namikawa (Poisson deformations and birational geometry). As observed in Kubrak and Travkin - Resolutions with conical slices and descent for the Brauer group classes of certain central reductions of differential operators in characteristic $p$, given a singular variety $Y$ over a field of char $0$ and provided there exists at least one symplectic resolution $\pi: X \rightarrow Y,$ the vector space $V_{\mathbb{R}}=\operatorname{Pic}(X) \otimes_{\mathbb{Z}} \mathbb{R}$ can be partitioned into a union of rational cones, and there is an action of a finite group $W$ on $V_{\mathbb{R}}$ that maps cones to cones. The set of symplectic resolutions $\pi: X \rightarrow Y$ is then identified with the set of cones modulo the action of $W$.