Sarnak's conjecture on Möbius disjointness along polynomial iterates

Let $(X,T)$ be a minimal topological dynamical system, meaning that for every $x\in X$, the set $\{T^n x\}$ is dense, with zero entropy. Let $x_0\in X$, let $f\in C(X)$, and let $p:\mathbb{N}\to\mathbb{N}_0$ be a polynomial. Polynomial Sarnak conjecture. One has

$$\frac{1}{N}\sum_{n=1}^N\mu(n)f(T^{p(n)}x_0)\longrightarrow 0.$$

This was proposed as a stronger polynomial-iterate version of Sarnak's conjecture, with minimality added to exclude degenerate examples. The source states that it is false, citing separate counterexamples of Kanigowski, Lemanczyk, and Radziwill, and of Lian and Shi.