Likelihood of Unscented Kalman filter
Your mistake is that $\mathcal Z$ does depend on process noise. It's just a bit more obscure than the linear filter. $\mathcal Z$ is the projection of the sigma points through the observation function. The sigma points are a $\mathcal f(P)$. Therefore $\mathcal Z$ is a $\mathbf f(P)$, and therefore related to $\mathbf Q$.