  We prove a generalization of the Jacobian criterion of Fargues-Scholze for
spaces of sections of a smooth quasi-projective variety over the
Fargues-Fontaine curve. Namely, we show how to use their criterion to deduce an
analogue for spaces of sections of a smooth Artin stack over the (schematic)
Fargues-Fontaine curve obtained by taking the stack quotient of a smooth
quasi-projective variety by the action of a linear algebraic group. As an
application, we show various moduli stacks appearing in the Fargues-Scholze
geometric Langlands program are cohomologically smooth Artin $v$-stacks and
compute their $\ell$-dimensions.
