For simple Shimura varieties whose local group is an arbitrary inner form of a product of Weil-restricted general linear groups, the Scholze test functions satisfy the expected vanishing and base-change properties, yielding the semisimple cohomology description.
The fundamental lemma for stable base change
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On the cohomology of simple Shimura varieties with non quasi-split local groups
For simple Shimura varieties whose local group is an arbitrary inner form of a product of Weil-restricted general linear groups, the Scholze test functions satisfy the expected vanishing and base-change properties, yielding the semisimple cohomology description.