I got the distinct impression that not-Sara had not "lived" at all; she was unconscious until they uploaded Sara's memories, and it was only the error in the transcription process that let her 'wake up' at all. She has no memories of her own; her life started when they brought her awake on the table, with scattered fragments of Sara's memories - incomplete and "unreal" to not-Sara - in her mind.
I loved this story but had the same impression, which had me wondering why notSara was so fixated on this idea of not being Sara when in fact she was Sara -- just an incomplete version suffering from a form of amnesia. Everything about notSara was derived from Sara, unless the clones somehow had their own experiences and existences before being wiped each time, which would be horrible. But I didn't get the impression that notSara had any experience or consciousness before waking up during the aborted procedure.
(By the way, I would speculate that I suspect that if such a thing happens again in that world, they would likely tell the half-cooked clone that they were in a bad accident, had amnesia, and it would be fixed soon.)
The real question I wonder about is when they finally upload the rest of Sara's memories, does that necessarily destroy all of the memories of her week without them? Or will they just be added to her mental filing cabinet? If just added to the filing cabinet, she really isn't dying at all, so no need to be sad.
Along those lines, she might be the first person this happened to, so there might be uncertainty about which way it would go, but this should be easy to test on animals. Clone a dog and wake him up halfway through just like with notSara. Then, ring a bell and give him a steak. Do that ten times until the bell ringing causes him to salivate. Then, finish the upload and ring the bell -- if he salivates, the new memories coming in likely don't destroy the memories of the intervening week.
On the flashback at the end, that confused me as well - I had no idea it was supposed to be in the past, and wish we can come up with some way for narrators to indicate something to alert us when that is happening.
Lastly, related to narrators, I thought Mur's reading was perfect for this story - she does a fantastic teenage girl -- almost as if she had once been one -- but I very often finding myself wondering why Mur does so many of the narrations herself when there are (presumably) so many great narrators and voice actors who would like to narrate the stories here? I find Mur's voice and style to be so distinctive that I often have a hard time separating her as "Mur" from her as narrator -- and I almost always prefer to hear someone other than Mur read the stories because that lets me concentrate much more on the story than the narrator.
It's kind of like seeing the same actor in five different movies in a year. It makes it hard to see them as their character as opposed to them as the famous actor. (I'm looking at you Denzel Washington and Paul Giamatti.)
All in all an excellent story.