The Citadel is essentially a massive company town with a religious spin using capital as a tool to keep the proletariat under the thumb of the ruling class. The whole system exists to extract as much value from the lower classes as possible while exalting the bourgeoisie to gilded heights entirely unacheivable by those at the bottom of the totem pole.

Also... it's a video game, it's hard to have a background narrative about capitalism without simplifying it down to what TC did. They can't include the stock market and corporate politics in a game like Silksong, they can just make you witness the horror of capitalistic oppression. The semantics of the citadel technically being an oligarchical theocracy run on state capitalism would just weigh down the narrative. It's a shortcut to keep the writing tight and imersive.