What I got from Zed's interactions is that he used to be a Templar who went against the rules of the order, consumed ora and was ultimately corrupted by it; he now seeks to build a world without conflict by making everyone become either one with the ora or... dead.
There's still something I don't understand tho: why does he feel the urge to kill the Cosmic bros and why do they want him dead? Was the ora he consumed somehow contaminated by Rhaast? GS Zed doesn't seem to even know what the Dark Stars are, so I would be inclined to rule it out.
What are your thoughts on this? My theory is that consuming large amounts of ora causes an individual to attune with all the other living beings infused with the golden substance, which leads them to lose their individuality and consequentially their sanity, turning them in schizophrenic serial killers. Thus GS Zed is a potential double threat to the galaxy: not only he's directly harmful to every living being, but he also could be used as an ora battery by Odyssey Kayn/Rhaast in order to open up a portal to the Dark Star/Cosmic universe.