I'd say the Klingons and the Feds both had a small cabal of warhawks in their midst, acting against the legitimate government - but the Romulans were in it lock, stock and barrel, with full governmental backing.
Klingons and Feds had been blood enemies for the better part of a century. Why had they not fought an open and decisive war yet? Apparently because neither side believed it would be sufficiently stronger to ensure a clean victory. But if one side or the other managed to ally with the Romulans, then that side could start a war with the confidence of winning.
Romulans would of course benefit from a war between the two foes that was not clean - a more or less evenly fought conflict where both sides would be mortally hurt. So it would be in their interest to secretly promise one side the full support of the Romulan Star Empire - and then secretly promise the other side the very same thing. That would make both sides go to war with false confidence.
That the Romulan Ambassador was part of the most secret war plans of the Federation goes to show that something like the above promise was indeed made to the Federation. That Chang dared go to war on his part suggests that he was promised more or less the same thing.
But Chang and Cartwright were also helping each other, because without such cooperation the respective governments would not agree to going to war yet. So Cartwright gave Chang what he needed for assassinating Gorkon (Federation-lookalike torps plus the presence of James T. Kirk), and Chang gave Cartwright an unfair trial of Kirk to anger the UFP leadership. But both also prepared for backstabbing, probably knowing fully well what the other was doing but not caring because both believed they had the secret Romulan ace in their sleeve...
A Starfleet conspiracy against Starfleet and a Klingon conspiracy against Klingons would both have been absolutely necessary for igniting the desired war. OTOH, there was no need for, and no evidence of, a Romulan conspiracy against Romulus. All the Romulan actions were for the greater good of the Romulan Star Empire, including the arranging of the Khitomer conference (apparently the doing of the Romulans, as their symbols presided over the venue).
Timo Saloniemi