de Rham mapping stacks of smooth projective varieties are geometric

Let $T$ be a very presentable geometric $n$-stack, and let $X$ be a smooth projective variety. Write $X_{DR}$ for its de Rham formal stack. The de Rham mapping-stack conjecture. The mapping stack $Hom(X_{DR},T)$ is geometric. The source calls this a more reasonable statement after listing broader conjectures, but supplies no evidence of a proof or disproof.