One thing that stood out in the way Sun-Tzu handled capellan inner politics was his constistency in seeking to divide his "inner circle". This COULD be linked to a certain paranoia, but it could also point out to how the different branches of the capellan system used to be constantly vying for greater influence whithin the confederation before the 4th SW, and this was still fresh on the celestial wisdom's mind.
It could be argued that the fact citizenship is actually something you ACQUIRE and hence has a lot of symbolic importance attached to it, coupled with the korvin doctrine (which in its contemporary form feels much like "everything within the state, nothing outside the state") and the state of constant desperation for survival in the face of bigger opposition then themselves makes the CC less subjected to armed conflict beyond coups. But political intrigues with aims other then simply toppling the top dog
can still be a thing.
Now as a few have pointed out, the 4th SW was rife with treachery and power grabs. St-Ives, the Tikovox Free Republic...but also the Northwind Highlanders, now that was one huge chunk. The gutting the CC suffered would, it is rather safe to assume, leave all powers save that of dear pugnacious Romano in a state of shock. Hence, after the 4th SW, CC inner politics are rather...tame.
But before Romano's time, things were far more interesting. Maximilian's rise to power of course, around which much "higher up" blood was shed and many of the higher offices changed hands. But in a broader sense, it is quite clear the few main branches of the state (Chancellor, CCAF, Warrior House, Death Commandos, Maskirovka, Prefecture and House of Scions) all had a knife at each others throats. Check and balance the Capellan way, if you will.
Of course, the CCAF stands out with Pavel Ridzik (whom WOULD make a power grab as it turned out), but there must hjave been much friction elsewhere. The maskirovka was lead by an ambitious woman who longed for the bygone days where her family held much sway over the fortunes of the capellan state and she had one of her agents posted as the "closest thing to a friend" to Maximilian.
Said "closest thing to a friend" (also known as Dolman Kavajk) was portrayed as constantly seeking to weaken House Master Karl Yadi, whom obviously believes he should be ready to militarly oppose Maximilian if such an opportunity arises.
Then there is the prefecture. While the chancellor sits at that office, he is more or less openly opposed (if we look at 3025) by at least 2 of the other members of this small body. We know how Candace was at odds with her father, at the very least in the economical sphere, and then there is Lord Hargreaves who even dared to oppose Maximilian taking the chancellorship from his father. Some of those meetings must've been explosive.
And of course the house of scions. While their temopral power is limited, being there (aside for budgetary concerns) mainly to point out things for the prefectorate and the chancellor to take notice, around 3025 there was at least Lord Hargreaves creating some turmoil, and we know that in the past the house of scions has had a lot of weight in policy making...weren't they responsible for the appointment of Kalvin Liao or another of those less palatable chancellor's?