[cwillu]

One example: at one point I woke up with utter certainty that nothing unusual had happened in the last hour, and I was rather peeved at how long it was taking to even start with the preliminaries. As in, my sense of continuity was from a moment significantly before the last moment I could later remember (!)

[feet]

That's only perception of continuity. I'm specifically speaking about physical continuity. Continuity of our physical system which has constant internal communication, this internal network dialog does not stop even when under anaesthesia.

Our continued awareness comes from being the same physical system when we wake back up even if you don't have memory of the events.