Serious world-building question here. No AI please that defeats the point of a discussion post and I genuinely don't need that.
If you are some sovereign ruler of an interstellar nation, how many levels of administrative units would be good to reduce red tape and lube the flow of paperwork?
On earth, most countries have 3 levels (states, cities and sub-city?).
What about an interstellar country?
I will put an example country so it is easier to discuss.
So Country Z has:
+1 capital planet: with as much people and geographic complexity as Earth
+10 major planets: about 4-6 billion people and several thousand cities each
+34 minor planets: below 1 billion people each (please note that major or minor refers to the population count and not the planet physical size)
+62 space stations: about several hundred thousand to millions of people each.
While I may not be intelligent or knowledgeable enough to really answer this in depth, I think I might have some ideas. Okay, so it seems like an Empire of sorts with a Sovereign leader. Honestly... I'd highly recommend into looking how the British Empire handled and ruled so many colonies across Earth.
And depending how realistic you wanted, entire swathes of planets likely would be shared with other powers rather than one sole government leader. Typically, Empires form because there are easy access points between areas of the Empire (like Egypt's Nile and the Mediterranean for the Romans) The reality is there's be an inordinate amount of red tape and administration that the Emperor would have to delegate for things to even run to any degree.
So if we look at the example: there's the capital planet with about 8 billion residents. On Earth we have 195 sovereign nations (not including territories and colonies, I am including Palestine). But then there's 10 major planets which would likely have (rough estimate) 100-200 nations each. So... (including minor planets) the Empire's rough estimate population would be a whopping 95 billion peoples.
Since it's an Empire, you would effectively have a royal family: each would have a sovereign leader over either the entire world, or for each continent; likely their children administrating the continents. So you're looking at a huge royal family, not to mention nobility who would then be those royal's vassals. You'd have probably about... 20 royal vassals with vassals beneath them. For Space stations, they would likely be controlled by generals under the jurisdiction of said Royal families depending on the distance of them to the planet; maybe a few would be directly controlled by the Emperor himself with his top generals for front lines.
Generals and other vassals of minor planets would also fall under the jurisdiction of the royal family, again, like the space stations. Those colonies would be focused on food and material gathering and production meant to be shipped back to the larger planets. These colonies (like real life ones) would inevitably rebel depending on how they are ruled and treated by laws and taxation.
If you have a parliament, it gets even larger. Let's estimate, like the US, that 5% of the population works as government workers of all levels. You'd have at minimum 4.75 billion government workers. I'm going to be real rough with military, but there'd be 500,000,000 actively enlisted soldiers (it'd vary depending on how much military infrastructure, again US assumed) Let's assume generals would be in charge of 100,000 soldiers, so you might have around 5000 generals minimum.
But honestly... the story would be more interesting if the system wasn't efficient. Efficiency is boring; chaos is fun. Empires thrive through constant warfare and expansion, so when they can't they fall apart due to their size. The Roman Empire lasted about 500 years, same was the Ottomans, and the Byzantines a huge 800. All of them were constantly struggling with revolts.
I'd recommend much smaller, because then it's more comprehensible to readers. Like I wouldn't want to know all ten planet names, and who is in charge, because it wouldn't matter (usually), and I'd get frustrated as hell if the systems were far too efficient and logical. People are dumb, unqualified, and even if the Emperor was a total genius, there'd be no way he could alone efficiently run everything and make sure all the proper people are in their place.
On earth, most countries have 3 levels (states, cities and sub-city?). To this point, no... It'd be Nation, states that make up the nation, and counties that form the state. Then there are cities in the county, then towns. Each town would have a mayor, each county might have a representative, etc.