The strict Weihrauch separation between finite and infinite iterations of NON

Let $\mathsf{NON}$ be the problem discussed in the paper, and let $\mathsf{NON}^\omega$ and $\mathsf{NON}^\infty$ denote its countable and inverse-limit iterations, respectively. The strict separation conjecture.

$$\mathsf{NON}^\omega\mathop{<_{\mathrm{W}}}\mathsf{NON}^\infty.$$

The paper has established related Weihrauch reductions, but the strictness of this comparison remains conjectural.