I don't know if political authority will flow up from the bottom or down from the top, or both, but the orbital habs should be organized in groups, and bigger groups, and even bigger groups and so on.
For example, 10 habs may make a first level unit, 100 habs may make a second level unit, 1,000 habs may make a third level unit, 10,000 haps may make a fourth level unit, and so on up to 100,000,000 habs making an 8th level unit, 1,000,000,000 habs making a ninth level unit, 10,000,000,000 habs making a tenth level unit, etc. etc. for as many levels as needed.
This table lists the levels of administrative divisions within each country:
In the USA there are three levels below the national level: state, county, and municipal. The table has four columns for levels below the national level and in some countries the fourth column includes two levels. Thus in present day practice there are up to five levels of administrative divisions beneath the national level.
Note that in the late Roman Empire there were also five levels of administrative division below the imperial level. A pagus was a subdivision of a civitas which was a city state with a republican form of self government formed out of a preexisting tribe or city, a group of civitates was supervised by a governor of a province, the governors of provinces were under the authority of vicars governing civil dioceses, who were subordinate to the four Praetorian prefects governing prefectures under the Emperor.
Note that in Star Wars The Galactic Republic ruled more planets than there were civitates in the later Roman Empire but had fewer levels of administration.
The most common organization for these new territories was to group regions into Sectors of about 50 inhabited worlds. Each sector is represented by a Senatorial Delegation. When the number of sectors became too large, sectors were organized into roughly a thousand regions, each represented by one delegation to the Senate.
So with about 50,000 planets in the Galactic Republic there are supposed to be only two levels of administration between the senate and an individual planet. And each senate delegation represented a region with a thousand planets. I have my doubts how well that would work.
I don't know how administration may work with seven, eight, nine, ten, or more levels of administration.
Theoretically a wide hierarchy could reduce the numbers of levels needed by having a a large number of subordinate units under each unit. For example, 100 habs in a first level unit, 10,000 habs in a second level unit, 1,000,000 habs in a third level unit, 100,000,000 habs in a fourth level unit, and 10,000,000,000 habs in a fifth level unit if needed. This would reduce the number of levels that orders and information are passed though, but it would make each level's task of supervising many units difficult.
Or in a narrow hierarchy, units at each level would supervise a small number of units on the next level down. That would be an easier task. But then a larger number of levels of administration would be needed, possibly more levels than have ever been made to work in human history.
In a government with many levels of administration, it is considered necessary to pass orders from the top down through many parallel hierarchies to be certain that the orders will reach the bottom and not be lost in transition.
In a Dyson swarm one of the hierarchies could be the Habitat Inspection Service that inspects the structural integrity of the habitats to make sure they aren't about to fall apart and perhaps damage other habitats.
Another hierarchy could be the Swarm Navigation Service that makes certain that all space ships travel on trajectories that won't strike any habitats if they fail to make course corrections.
There could be a Swarm Space Navy or Swarm Space Guard to protect against invasions from outer space, defeat rebellions, and vaporise any spaceship with a trajectory calculated to impact on a habitat. Note that if a one "star" admiral commands the naval forces in ten habitats, for example, the highest ranking admirals might be at least seven "star" admirals, unlike in modern navies.
There could be a Swarm Security Service to investigate any possible plots to revolt or commit terrorism.
And maybe a Swarm Intelligence Service to investigate any possible plots to revolt or commit terrorism.
And the Swarm Security Service and Swarm Intelligence Service would also investigate each other to make sure they are doing their jobs properly.
And the Swarm Space Navy or Swarm Space Guard might have an intelligence service that investigated crimes, rebellion, terrorism, and the other spy agencies.
Clearly the government of a Dyson swarm could have a complexity similar to that of a science fiction galactic empire.
And if you write about a Dyson swarm or space empire with a monarchy, remember that unlike the usual idea in western civilization, a king is not the next step below an emperor. If the space realm has kings above dukes, it is likely to have kings of kings - or second level kings - above kings, kings of kings of kings - or third level kings - above kings of kings, and so on up to the empeor who might be equal to a tenth level king, for example.
If the Emperor claims to be the rightful ruler of the universe, he might use hundredth level king or king to the thousandth power as one of his minor titles, even if his realm has far fewer than a hundred or a thousand levels of administration.