It seems to me that Gavilar is the link between all the groups and organisations across Roshar. He possessed a certain knowledge which he ironically shared with everyone but his own family which now has kind of formed the Knight Radiants. Starting with the followers of Diagram, we see that Taravangian in his moment of reflection after he becomes the king of Jah Keved thinking about how he had followed Gavilar’s instructions to unify the world for survival and he also knew that Gavilar had visions from Honor which foretold of the Everstorm.
Also, Amaram when he sneaks in to inspect Taln and steal the shardblade wonders that the heralds are real and murmurs “Gavilar, we have done it. We have finally done it” which leads me to think that Amaram and Sons of Honor’s motivations are also linked to Gavilar. Though I don’t know what exactly Gavilar has shared with them, probably something about the return of the Heralds and facing the Desolations. This could be something similar to what the Envisagers wanted maybe, where they tried to bring back Knight Radiants the Restares are trying to get back the Heralds, I mean they want the dominance of the Church and they would want their Gods back to help them survive.
The Parshendi of course knew what Gavilar was planning. On the shattered plains when Adolin was facing Eshonai in his father’s shardplate, she says that Gavilar was trying to bring their gods back and that would have led to complete destruction. As their gods had once forced the forms upon them and the only way they could have freedom was by devolving to the dullform. (this makes me think that the Parshmen and Parshedi are of Odium).
Even the Ghostbloods, before dying Gavilar thought Szeth was sent by Thaidakar, the man who leads the Ghostblood.
And the Heralds were also involved as Nalan was there at the treaty signing party and they were discussing how their conditions are getting worse specifically mentioning Ash (shalash). Also, Nalan reveals to Lift that what she is must be stopped as it would return desolation so maybe they were there to stop Gavilar as he wanted to refound the Knight Radiants.
So, it seems to me like every road leads to Gavilar. Something is happening that all these secret societies know and Gavilar was the trigger that started the chain of events by discovering the secret that led to his assassination by the Parshendi bringing the fate of Roshar together. And now everyone is either following or trying to stop Gavilar’s work by attempting to unify mankind or trying to stop the desolation.