Oh, that's the core of the entire genre, isn't it? It's never just about a crown on a head.
The most obvious theme is power as an illusion of legitimacy. Characters constantly perform power—through lavish feasts, brutal public executions, or strategic marriages—to manufacture consent from the nobility and fear from the populace. The one who seems most powerful is often the most vulnerable, because their position is a glittering target. Think of the Lannisters in 'A Song of Ice and Fire'. They have the throne, but their power is a precarious house of cards built on debt, lies, and the temporary loyalty of bought swords.
Then there's power as intimate knowledge. The real rulers are often the spymasters, the court scholars, or the forgotten second sons who have spent a lifetime learning everyone's secrets. This power is quieter, often more feminine-coded or perceived as 'weak', but it's the knife that slips between the ribs during a private audience, not on a battlefield. It's the power of knowing which guard is in love with which maid, and what that debt can be leveraged for. Betrayal here isn't a sudden act; it's the currency of these hidden networks.
Finally, the most fascinating theme to me is power as a corrupting self-betrayal. The protagonist often starts wanting to fix the kingdom or claim their birthright for noble reasons. But to survive the blood and the betrayals, they must become fluent in its language. The true tragedy is watching them win the game by sacrificing the very principles that made them root for their own rule. The power they sought ends up hollowing them out, making them a mirror of the tyrant they replaced. The ultimate betrayal is the one they commit against their own soul.