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Could probably set this up outside of the facetwp plugin. Plenty of plugins to notify users of new posts that meet certain requirements.
Content Notify is probably your best bet: https://contentnotify.com/
If that plugin doesn't integrate with FacetWP, perhaps their team could consider adding it.
My biggest concern would be server load. Having to calculate whether a post matches against potentially thousands of saved facet searches could prove EXTREMELY server intensive.
Are you referring to email notifications?