Artin's precise flat duality conjecture for surfaces

Let $\pi\colon X\rightarrow\operatorname{Spec} k$ be a smooth complete surface over a perfect field $k$ of characteristic $p\neq0$, and let $R\pi_*\mu_{p^n}$ be the derived flat-cohomology object viewed in the category of commutative group schemes over $k$ modulo infinitesimal group schemes. Artin's precise flat duality conjecture. There is a canonical isomorphism

$$R\pi_*\mu_{p^n}\rightarrow R\operatorname{Hom}(R\pi_*\mu_{p^n},\mathbb{Q}/\mathbb{Z})[-4]$$

in the derived category of that quotient category. The source states that Bragg and Olsson (2021) proved this precise statement.