I've been thinking,...
Chaladon probably has some sort of religion governing them, but the religion has a strong affinity to science.
Yesha wouldn't follow Confucian ideals. Sure, they seem very East Asian, but Yeshan ideals of meritocracy and ambitions are in direct conflict with Confucian ideals of hierarchy and knowing-your-place. My guess would be that Yesha would have something similar to the one-party system China currently has. A system where government offices are mostly based on merit, but similarly riddled with corruption.
Mercantile Guild is probably Italian city states bound under one ideal of profit.
Anglea, I think, probably doesn't have a formal government.
Baronies are probably Feudalism and Manorialism. But I wonder if they have a king. If they do, the king wouldn't be an absolutist, but a weak monarch similar to the elected, non-Habsburg Holy Roman Emperors.
Arashi, probably similar to Anglea.
In fact, what is the difference between Arashi and Anglea? They are both raiders and pirates. Barbarians and Hill People refusing proper civilization for freedom. What is different between Arashi and Anglea? Do they have conflicts?