Conjectural endoscopic Mantovan formula

Let $(G,b,\mu)$ be the local Shimura data appearing in the paper, let $\mathcal{H}^{\mathfrak{e}}$ be an endoscopic datum, and let $\operatorname{Mant}_{G,b,\mu}$ and $\operatorname{Red}^{\mathcal{H}^{\mathfrak{e}}}_b$ be the Mantovan and reduction maps used in the paper. Conjectural endoscopic Mantovan formula. One has

$$\operatorname{Mant}_{G,b,\mu}\circ\operatorname{Red}^{\mathcal{H}^{\mathfrak{e}}}_b=[\mathcal{M}_{\mathcal{H}^{\mathfrak{e}},G,b,\mu}]$$

in $\operatorname{Groth}(G(\mathbb{Q}_p)\times W_{E_{\{\mu_G\}}})$. This extends the previously discussed formula in the trivial-endoscopy setting to nontrivial endoscopy; the source presents it as conjectural and gives no resolution status.