I encountered this problem very recently as well. I like receiving notifications for Breaking News but I don't need notifications for lifestyle suggestions. Unf

I encountered this problem very recently as well. I like receiving notifications for Breaking News but I don't need notifications for lifestyle suggestions. Unfortunately there is no classifier for this in the News App. My workaround was to go into the settings for News and turn off notifications for every media outlet other than the New York Times. It's definitely not fool-proof but keeps more sane. There however seems to be no way to automatically get rid of notifications on my iPad once I have read them on my phone...