Han's decomposition and temperedness conjectures for Langlands–Shahidi parameters

Let $\varphi\colon W_F\to{{}^LG}({\overline{\mathbb{Q}}_\ell})$ be a semisimple $L$-parameter of Langlands–Shahidi type, and let ${\mathcal{F}}_\varphi$ be the corresponding Hecke eigensheaf. For each $b\in B(G)$, let $G_b$ be the associated inner form, let $\Pi_\varphi(G_b)$ be the corresponding packet, and let $i^{b,\operatorname{ren}}_!$ and $i^{b,\operatorname{ren}}_*$ denote the normalized extension functors. Han's conjectures. There is a decomposition

$${\mathcal{F}}_\varphi=\bigoplus_{b\in B(G),\,\pi\in\Pi_\varphi(G_b)}i^{b,\operatorname{ren}}_!\pi^{\oplus m(\pi)},$$

where each multiplicity $m(\pi)$ is finite and nonzero, and every summand satisfies

$$i^{b,\operatorname{ren}}_!\pi\cong i^{b,\operatorname{ren}}_*\pi.$$

These are cited in the source as Han's Conjectures 2.1.8 and 2.1.9. Their resolution is not specified in the paper.