Regarding the matter if Kusari is (was) an Empire, or a Shogunate: While a Shogunate can be a form of government (like a military junta, or a dicatorship), it is not a form of State. Therefore, Kusari for all purposes was an Empire.
On the matter of who is the boss: This question has been raised on the development channel of Kusari, on matters relating to KNF and Samura, and on the concept of the Exiles.
We were faced with the same gaps related as to the "original" form of state that Kusari took after planetfall. There is not direct lore written regarding anything before the Sakura coup, other than the origins and "player written lore" of Samura and Kishiro.
It also struck me as odd that, being an empire, the deposed element of the Dragons was a Shogun, and it's not clear if this Shogun held power on his own, or under the legitimacy of a puppet emperor in the background. Same as the vanilla Shogun Edo that you have researched.
There is also very little lore available about the rest of the political systems of the Settlement Regime, the Hideyoshi Shogunate, or the post Sakura/Vanilla government, other than the mention of the Prefects/Governors. No mentions of nobility, ministers or territorial divisions, other than the faint allusion to the current Prefectural System.
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Of course, such gaps have left plenty of space for everyone to imagine how the past shaped the present, and added their own flavor. Imperials have built an image of a despotic Emperor, one that takes to the battlefield like some crusader king. Many Dragon players roleplay old nobility families disgraced by the Sakura coup, wishing to recover their "Planet sized titles" of ownership alongside to the return of a Shogun (or Shoguns?, every incarnation is a new Shogun family).
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Devs of old never bothered to reshape the old storyline of Kusari, to fill up those continuity gaps. I can't say it is a bad thing, but probably it was the wisest choice, if it was ever pondered.
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