Okay, my actual prognosis on the situation if we somehow win and depose the HSE.
The United Solar Empire will severely stress its administrative and military capabilities during and after the war, which it already attempts to supplement by allowing native Saturnians to serve and actually advance the ranks. They already don't have enough ships to saturate the entire solar system, and the situation won't improve much after epic anime battles in the orbit of Mars and Earth. On the other hand, people capable of administering the planets and the stations also seem to be in short supply, since more than half of noble families, the traditional landholders in anachronistic settings, are on the enemy's side ( under the threat of violence or otherwise. )
Likely, the government will decentralize, with the new capital moving to Saturnian subsystem, since Princess would be pretty stupid not to attempt and secure her seat of power that she and her aunt organized the insurrection from. Besides, Saturn is a frontier, with no potentially hostile aliens lurking in the shadows of Uranus and Neptune, that's for the sequel series.
Jupiter is very likely to demand increased autonomy and its own governing council, not staffed by nobles. In contrast, with decrease of noble families, the individual holdings on Moon and Mars will proportionally increase, unless Daystar somehow breaks the feudal system over her knee and establishes direct Imperial rule or something.
So, in the end, Earth will be a provincial and an overcrowded backwater everyone wants to get away from, Moon and Mars will be divided between petty principalities with significant populations, Jupiter will become Hansa, but in SPEEEEEHS, and Saturn will be a new center of expansion and scientific innovation, with the whole structure more resembling a confederation than a single monolithic entity.
Lol, unless we fail, die and the HSE disintegrates into a post-apocalyptic collection of warring states. Mad Max on Mars when?