The Sooni Zealouts are a dangerous group of Sooni religious fanatics who believe The Overseers to be gods, and strictly follow their teachings with no room for interpretation. They believe that humanity needs to be exterminated; they see humanity as an affront to The Overseers's will. They believe the Sooni's rule should be absolute and that The Overseers intentionally raised the Sooni above all others. They view any Focus use by humans (or other races) as an 'abomination'.
The Zealots started out as a simple group of hardline religious fanatics worshiping The Overseers. They took very literal interpretations of everything and saw no room for interpretation.
This naturally evolved into a group of extremists that fought to control the Sooni people. However because of their extreme views and methods, they didn't gain much influence for a very long time.
After the war with The Grey it was the zealots who first showed the rest of their people how to regain their power. They learned how to indoctrinate The Grey and over the next three thousand years proved instrumental in helping the Sooni escape from their captivity. Since the zealots were simply a group who agreed with each other and not a real organization, none of them capitalized on this moment, but their views were much more popular while the Sooni were enslaved.
When the Sooni rediscovered humanity, the zealots took a hard line on their existence. They wanted humanity destroyed, seeing their very existence as a heresy against The Overseers. While the moderate Sooni eventually one the discourse, the idea that humanity existed at all was a shock, and seeing how technologically backwards and societally inferior they were was disturbing to many Sooni. There was something appealing about removing this "flawed" version from existence.
This marked the first official organization of the zealots; they capitalized on that and worked very hard to try and influence the Council to see things their way. While it didn't immediately work, they had far more voices in the Council than they ever had before.
It was the Zealots who suggested the policy of stewardship to begin with. When it became clear they couldn't win the political argument to destroy humanity, they backed the much less extreme idea that in order to protect humanity, other races had to be influenced. They knew it was a simple jump from this to the inevitable policy that humanity itself had to be influenced.
After the First Interstellar War, the Zealots made the argument for direct interference with humanity's development. It was done under the guise that the influence would simply be to protect humanity, and they had enough of their members fight against it to make it look legitimate.
Since the Zealots had their first win, their ultimate goal has been the destruction of humanity and complete control over the Council. They have multiple plans and smaller groups that fall under the same name, each trying to push a winning tactic. At the end of the day they don't care how it happens, they just want humanity to burn.