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If Mayuri had died, wouldn't that create a time paradox? Since the only reason Kagari was there was because Mayuri adopted her in the future; a future in which she needs to live? At the very least it definitely would've triggered Reading Steiner to move the worldline in some way.
As for whether she went to the past or future, hard to say. Either way, wherever they end up clearly does not change the future.
Also, Kagari proved herself to be basically filler yet again. She served no purpose other than providing information to the Professor, and could have just as easily been dissected then and there. The current story wouldn't really change in the slightest other than a couple less filler episodes. What she did here, Suzuha could've done. But whatever, unless a Time Leap is done she's at least gone so we can get to the meat of the story.
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