Polynomial Sarnak's conjecture for minimal systems II

A minimal topological dynamical system $(X,T)$ has polynomial entropy zero when its sequential topological entropy is zero along all polynomial sequences. Let $(X,T)$ be a minimal topological dynamical system with polynomial entropy zero. Polynomial Sarnak's conjecture for minimal systems II. For every $f\in C(X)$, every polynomial $p:\mathbb{N}\to\mathbb{N}_0$, and every $x\in X$,

$$\lim_{N\to\infty}\frac{1}{N}\sum_{n=1}^N\mu(n)f(T^{p(n)}x)=0.$$

This weakens the entropy assumption from ordinary zero entropy to polynomial entropy zero while retaining minimality. The source presents the assertion as a conjecture, gives no resolution, and notes that it is false without minimality.