Essential Dimension and Faithful Rank of Finite p-Gerbes

Let $p\neq\operatorname{char}(k)$. We extend the Karpenko--Merkurjev theorem from classifying stacks of finite $p$-groups to arbitrary finite gerbes whose geometric inertia groups are $p$-groups, without assuming that the gerbe is neutral or that its band is represented by a group scheme over the ba