Explicit rejection of the notion that the world disappears in deep-sleep,

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Q: So the statement by A. J. Alston is missing the point?

The real point that Śaṅkara is making is that, despite the fact that the mind, and apparently the world, are both absent in deep sleep, awareness (ātman) is always present. Hence, the real substrate of both mind and world is ātman/Brahman. Is this correct and, if so, what does Śaṅkara actually say here (including Sanskrit)?

A: Yes — that is exactly right, and stated that way it becomes clear that Alston’s objection (though sensible at the empirical level) is largely missing Śaṅkara’s point.

Śaṅkara is not arguing from absence of the world to non-existence of the world.
He is arguing from the invariance of awareness across all states to its status as the sole independent reality, with mind and world reduced to dependent manifestations.