  We develop a theory of Smith-Treumann localization and relative parity
sheaves in the context of Fargues-Scholze's Geometrization of the Local
Langlands Correspondence. We then apply this theory to prove some conjectures
of Treumann-Venkatesh concerning mod-$\ell$ Local Langlands functoriality
between a reductive group $G$ and its fixed subgroup under an order $\ell$
automorphism. As another application, we calculate the Fargues-Scholze
parameters of mod-$\ell$ Howe-unramified toral representations.
