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> the doctor explained to me that I would be awake for part of the procedure, but the anesthesia meant that I would have no memory of it

The short story "Transition Dreams" by Greg Egan touches on this concept

I can strongly recommend reading... anything else by Egan, just not that one.

It's not that it's bad. The problem's the opposite: He poses an existentially dreadful question which I can't definitively answer with 'no'.

That's what I love about this short in particular. Existential Sci-Fi!