In the case of a K3 surface, the representability of $R^2 \pi_\ast \mu_p$ is proven in the paper "Twistor Spaces for Supersingular K3s" by Daniel Bragg and Max Lieblich.
What you want is Theorem 2.1.6: If $\pi : X \to S$ is a relative K3, then the fppf sheaf $R^2 \pi_\ast \mu_p$ is representable by a group algebraic space, locally of finite presentation over $S$.