There is no now on earth, as each point on earth has its own light cone disjoint from everyone else's. Of course that these light cones intersect quite a lot, and because of this intersection you are free to declare a region of small spacetime around an observer as "now", provided that it is within the intersecting region. Of course when you do this you invent an ontologically distinct notion of now that very different from
any set of points of equal time coordinate in GR. And this notion of now is very useful for us on earth, for sure, but its definability depends on exactly how much the light cones on earth interact, and when you deal with events that don't interact this notion becomes meaningless.
When you talk about equal-time coordinates in GR, the notion of now is non-unique, and this is interesting, but popular articles fail to convey this.
When you talk about the human notion of now, the notion of now is local, it's not that this notion of now in astronomical phenomena is different, it's that it can't be defined at all. Popular articles not only fail to convey this, but give the impression that it can be defined. It can't, and that is what is interesting.
There are multiple levels of category error happening simultaneously. The confusion between equal-time surfaces, and neighbourhoods (4-volumes) around points, along with the conflation of a point with its neighbourhood. And from these popular articles fail to convey the interesting properties of either -- the observer's choice in defining surfaces, and that 4-neighbourhoods can't be extended arbitrarily far while preserving their topological properties.