I honestly have no idea aside from Inazuma and Liyue, I know Liyue is an Oligarchy, the wealthy lead to set an example, and qualification is shown by wealth.
And inazuma is like a mix of a theocracy and a military dictatorship to me, with the shogun leading by being powerful, controlling the military and being an archon. Maybe a shogunate, hence her title but I know nothing about those tbh so idk.
The other, I have no idea tbh.