It's quite literally a rebellion. Cass and her supporters had full control of the court and the palace, you escape gather support and fight against her. That's the definition of a rebellion.
The red vs white vs green has literally nothing to do with your methods. Green path and Red path are literally the same thing but one is under cath's influence and the other is you making your own choices while white is simply just the player not making any underhanded tactics to achieve their goal, vs the ends justify the means reasoning of the other two.
Also no, using a coup to take control is not "lacking in diplomacy" not really sure how you arrive at that conclusion. Coups have literally nothing to do with diplomacy at all. Unless your simply just supporting a pre existing plan for a coup, which is not only direct diplomacy but also involves a lot of diplomacy skills.
But the white emperor path is not supposed to be the "peaceful approach" path and the red Emperor is not supposed to be the "bloodshed path". It's just about your morals in regard to how you rule.
Alright, let's get one thing out of the way. The definition of a rebellion, a Rebellion is an armed action against a
Government or State, Cass is neither of those. She is a usurper who forcefully took power under false pretenses and with military force therefore it is quite literally not possible to mount a rebellion against her. What you
did however do is act like a good little loyalist and fought back against someone attempting to usurp the throne, this isn't a debate this is a simple fact. Cass had taken control of the capital and literally nothing else at this stage, she did not cement her position of power nor did she have control of the country therefore she isn't leading the nation.
As for your second point, to a limited extent your right. You still have freedom of choice, however of the two paths red is far more violent and bloodthirsty when compared against the White path, with the White path you are realistically following the laws of the nation and are the lawful leader, in neither of the other ones are you where you should be at all. It would not surprise me in the slightest if we got path specific options for the Red path which're far more brutal then the other two as that despite what you seem to believe is what it's there for.
I'm honestly not to sure what you were trying to say with your third.
using a coup to take control is not "lacking in diplomacy" not really sure how you arrive at that conclusion. Coups have literally nothing to do with diplomacy at all.
I'm guessing you completely missed the sarcasm in what I said somehow but I guess I can explain it directly. I was using it to lead further credence to my statement that the Red path was one of warfare and bloodshed not peace since as you so aptly put Coups do indeed have nothing to do with diplomacy, funnily enough armed takeovers aren't diplomatic.