Well, RE6 was the last game about Neo-Umbrella. That felt more representative of RE than what 7 and 8 focused on.
It was the first game about Neo-Umbrella as well. Because this is a criminal syndicate, the intents and purposes of which were not connected with the organization founded by Spencer and his colleagues. Just like Carla herself and her agenda had nothing to do with the ideas of Umbrella's doctrine in any shape or form.
Biohazard 6 was a game about The Family in the first place, and Neo-Umbrella was a faction of this shadowy organization that was established to conflict with Simmons and destroy the world, because Carla herself wanted it.
This plot and these organizations are relevant to the series just as much as The Connections, which was founded by Spencer's right-hand man, and Miranda's cult, which inspired Spencer. These organizations don't need to be called Another Neo-Umbrella or Umbrella's Forerunner to become more important than they already are.
And yet in BIO7 and Village there is an actual Umbrella, which, under the leadership of Wesker or his impostor, continues to build Spencer's dream of the evolution of the human species and utopian order. Does this not represent a series for you?
And what about those item boxes, electrocardiography, resources for saving progress and other countless nuances that make BIO7 and the game after it related to the series thematically and mechanically?
BIO6 is different from these games because the developers did homage to the incident in Raccoon City. That's why the game had a zombie apocalypse theme. It's cool, but other titles don't have to revolve around this theme, like the whole series. You yourself complain that developers don't stop milking Raccoon City, but why should they stop doing it if you yourself need Zombies and "Raccoon City" to "feel" the connection?
Something else Capcom will never bring up again, by the way.
Because it has already been done. Glenn Arias assimilated Neo-Umbrella and was defeated. I don't really know what other conclusion anyone needs, since this syndicate was merely a tool for Carla. It's not that important without her, and Carla's story was concluded in BIO6 itself. This is as strange as asking for the development of the cult of Chernobog after Miranda's death.