I don't think the supernova is supposed to be a mystery. That's just a plot point that was carried over from the 2009 movie, where it was portrayed as a natural phenomenon. And so far nobody on PICARD has indicated that there was anything mysterious about it (as opposed to the Mars Attack). The supernova is relevant because it led to the whole Romulan evacuation crisis, but what caused the supernova is not being presented to us as a mystery.
The other big mystery is: Who or what attacks civilization who cross a certain a threshold by creating synthetic life?
As I understand it, it's the not the synths who are the real threat. It's whatever lashes out whenever a species develops synthetic life. (See the analogy to Cochrane inventing the warp drive, thus attracting the attention of the Vulcans.)
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