Scholze's uniqueness conjecture for six-functor formalisms

Let $E$ be a class of morphisms, and suppose every morphism $f$ in $E$ is $n$-truncated for some integer $n$ possibly depending on $f$. Let $I\subseteq E$ and $P\subseteq E$ be classes such that every morphism in $I$ factors as a morphism in $I$ followed by a morphism in $P$.

Scholze's uniqueness conjecture. The six-functor formalisms produced by the Liu–Zheng construction are exactly those for which every morphism in $P$ is cohomologically proper and every morphism in $I$ is cohomologically étale.

The question concerns whether the intrinsic classes of cohomologically proper and cohomologically étale morphisms characterize precisely the six-functor formalisms arising from the Liu–Zheng construction, under the stated truncation and factorization assumptions.