All great points as always.It is definitely an issue with Elite Dangerous in-game storytelling.
Official books which have been approved as canonical say they exist (and the Oresrians too). Nothing in-universe says they exist except in the vaguest terms - you wouldn't necessarily conclude that this article and the beacons in Teorge refer to the same shadowy conspiracy, for example, or that either is the same as the Azimuth/Pharmasapien/Black Flight group being revealed recently [1] - but obviously any shadowy conspiracy worth talking about isn't going to have a public presence.
In more conventional games about conspiracies, well, fine, the purpose of the game story is to uncover the conspiracy so you find out more as you go along, and by the end (after a few days or weeks of play) you hopefully have a satisfying story.
In Elite Dangerous we're still barely out of the prologue as far as that goes, because of the necessarily slow pace of revealing things - and the Club, if they exist, are still so well hidden as to not really be dramatically necessary anyway.
I think this is why stories like Enclave or the NMLA arc - or on the mystery side, UAs or Azimuth - work better: you might not necessarily know all the consequences of your actions in advance, but at least you can make a logical guess at the short- and medium- term ones, and you get to see things change as a result.
[1] I don't think there's any actual reason - speaking solely about lore revealed in-game, not through official fiction - that the Azimuth/Black Flight conspiracy, the Core Dynamics/Vincent/Jupiter one, and the Dynasty/Exodus one couldn't all have been different groups.
I'm not a particular fan of "grand conspiracy" stories and I think they work very badly within ED ("blaze your own trail but they all support the Club in the end") so a broader set of secretive groups each with their own agenda and at best partial knowledge of each other is probably more fun anyway.
Kinda like "The Company" you see referenced though out all of Elite Dangerous's story's in logs and messages. Though its so vague it could just be the character saying the company or they could be saying "THE COMPANY".
But thats just a theory ! Not lore