More like a just over a sixth, there's three branches, executive, legislature, and judicial. If you buy into the whole "media is the fourth branch" thing, I say that's actually a minority or a plurality.
If you think "complete functional control over the supreme court for likely decades" is insignificant enough to make conservatives count as a minority you need to pay more attention to the powers and impact of the supreme court. They can effectively overrule any legislation if they wish and have proven a desire to do so.
They say they can do that (judicial review is kind of not in the constitution) but what California and New York are doing post New York State Rifle & Pistol Association, Inc. v. Bruen puts a bit of a question on that. Making much of New York City a "gun free zone" is not what "the right to keep and bear arms" sounds like to me.
I’m counting executive branch, judicial branch, and congress as two because they each individually have their own mandated powers.
The conservative Supreme Court just unilaterally gutted fundamental human rights for everyone in the country. That’s serious power that not even the President has. It’s a joke to pretend conservatives have no political power in the face of that.
The third highest government official is the Speaker of the House, who will be a Republican in January, so it’s pretty hard to say Republicans have no power when they control the Speaker. It’s crazy how much power that is.
But to call the media a branch of government and to assign “control” of media to Democrats is really a stretch. Pretty hard to make that case with Fox News around.