To a certain degree, governments like the Federated Suns and Draconis Combine are fictions. They exist at a very high level of abstraction. Historically, these were small empires that grew and absorbed neighboring entities either through conquest or mutual defense pact. Duke Stuffypants is granted control over the world Backwater V by the Coordinator. But that's because he already had control over Backwater V. Before he became Duke Stuffypants, he was Dictator-for-life Stuffypants. He joined the Combine in a mutual defense agreement and got official recognition of his claim, rather than risking war. And he and his descendants have kept that iron-fisted control over that world. To the people of Backwater V, the "Combine" is some far off entity that doesn't have much affect on their day to day life.
In other words, I don't think you'd have any politics at a national level the way we do today. Everything is too far removed. Modern politics (avoiding any specifics here to dodge Rule 4) revolve around what kind of policies people want to see implemented on a national level. But most of those policies would be implemented on a planetary level in the Inner Sphere. Many of the planets would be so different from one another that the issues just wouldn't translate.
A lot of the Great House politics are personal. The 0.000001% have enough personal wealth and power to start interstellar wars. And sometimes they do it because that guy slept with your sister, and screw that! It doesn't matter what the civilian population thinks. Even if you don't like Duke Stuffypants, he's got a massive army and that's that. If he wants to invade a neighboring territory, that's between him and the Coordinator. Besides, the other side also has a Duke Stuffypants equivalent, and that guy just might decide to invade your world as well. There's nothing you can do about it, so just hope your guy makes good decisions.
As a result, the mass media beyond a planetary level would probably be more like gossip magazines than the political talk shows of today. Think British Royal Family stuff, except if the Megan Markle situation was actually threatening to bring the USA and UK to war with one another.