DT4 square-root Euler class conjecture for $-2$-shifted symplectic derived schemes

Let $\boldsymbol{Y}$ be an oriented $-2$-shifted symplectic derived scheme, set $Y=t_0(\boldsymbol{Y})$, and suppose the dimensional reduction conjecture holds. Let $\sqrt{e_{\varphi}(\mathbf{T}^*[-1]\boldsymbol{Y})}\in\operatorname{H}^{\mathrm{BM}}_{\operatorname{vdim}\boldsymbol{Y}}(Y)$ be the Borel–Moore homology class obtained from the resulting composition, and let $[\boldsymbol{Y}]_{\mathrm{vir}}^{\mathrm{DT4}}\in A_{\operatorname{vdim}\boldsymbol{Y}/2}(Y)[\tfrac12]$ be the DT4 virtual class. Square-root Euler class conjecture. If $Y$ is quasi-projective, then there exists a universal sign $\epsilon_{\operatorname{vdim}\boldsymbol{Y}}\in\{-1,1\}$ depending only on $\operatorname{vdim}\boldsymbol{Y}$ such that

$$\epsilon_{\operatorname{vdim}\boldsymbol{Y}}\cdot\sqrt{e_{\varphi}(\mathbf{T}^*[-1]\boldsymbol{Y})}=\operatorname{cl}_Y([\boldsymbol{Y}]_{\mathrm{vir}}^{\mathrm{DT4}}),$$

where $\operatorname{cl}_Y\colon A_{\operatorname{vdim}\boldsymbol{Y}/2}(Y)[\tfrac12]\to\operatorname{H}^{\mathrm{BM}}_{\operatorname{vdim}\boldsymbol{Y}}(Y)$ is the cycle class map. This identifies the proposed sheaf-theoretic class with the DT4 virtual class up to a universal sign, but the supplied text gives no resolution status.