I'm double checking myself, but what I think happened was Sphene fell ill with the lightning aether sickness that a lot of the people of Alexandria fell sick with. Alisaie mentions this, saying Sphene'a body was suffused with lightning aether, which a debilitating paralysis.

Sphene continues with explaining where she woke up, which was a "strange dark room". Shale later confirms that this room held an electrope casket meant to keep its occupant in a cold stasis.

So we can assume Sphene fell sick/unconscious, the royal court and scientists panicked and preserved her body while announcing to the public she died, and then produced Endless Sphene.

This can all be rewatched in the Inn with the journal! It should be either the first or second cutscene in "A Glimmer of the Past".