The twisted K3 categorical rationality conjecture for cubic fourfolds

Let $X\subset\mathbb{P}^5$ be a smooth cubic fourfold, let $\mathcal{A}_X$ be its K3 category, and let $(S,\alpha)$ be a twisted K3 surface, with $\alpha\in\operatorname{Br}(S)$. Twisted K3 rationality conjecture. $X$ is rational if and only if there exists an exact linear equivalence

$$\mathcal{A}_X\simeq D^b\operatorname{Coh}(S,\alpha).$$

The source calls this a more provocative speculation intended to allow more cubic fourfolds to be rational; it notes that the conjecture would predict rationality for every cubic fourfold containing a plane, while the absence of such a result is presented as evidence against it. No resolution is stated.