By consciousness being an illusion I mean that we place great value on the uninterrupted continuation of our consciousness, but I think it's likely that it (exactly as you suggest) only really exists in the moment. The illusion would then be the illusion that consciousness is uninterrupted, when in reality you're almost constantly recreating yourself from memory.

This would, incidentally, make us concerningly similar to current AI models.

Of course I have no way of actually knowing any of this. It's just what I'm betting on, because otherwise I think it's really hard to explain any unconsciousness (be it sleep, general anesthesia, suspended animation or the Star Trek transporter) as anything short of death. My belief "solves" this problem by rejecting the whole premise of uninterrupted consciousness.