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Today I had the same idea of including stable (ir)rationality. For the record: Voisin proved in "Unirational threefolds with no universal codimension 2 cycle" that https://www.fanography.info/1-12 is stably irrational.
As explained in https://arxiv.org/pdf/2401.06577.pdf, stable rationality of cubic 3-folds is not known.
In general, information on (ir)rationality should be more detailed I think, with its own explanation page.
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