Higher-dimensional Shokurov-type conjecture for standard conic bundles

Let $\pi \colon X \to S$ be an $n$-dimensional standard conic bundle with $n \ge 3$, and let $\Delta$ denote the discriminant divisor of $\pi$. Higher-dimensional discriminant conjecture. If

$$\left| 2 K_S + \Delta \right| \ne \emptyset,$$

then $X$ is not rational. If, in addition, $X$ is very general in its moduli, then $X$ is not stably rational. The first assertion extends the preceding three-dimensional criterion, while the very-general assertion proposes stable non-rationality in higher dimensions; the source presents this as a question motivated by its results, and no resolution is supplied.