Humanity has access to a stargate of unknown origin. Each gate leads to a solar system from which other gates can be accessed, creating a kind of highway spanning some 300 systems. The travel time in solar systems is quite fast, in the solar system you can travel from the sun to the gate always located on the border of the system in about 1 month. How much an empire directed from the earth could grow effectively. I think of a British-style system, governors in systems that have to wait for orders but with autonomy. The fuel for ships is equivalent in abundance to oil, so some systems are more abundant than others, which favors space traffic, since it is quite light, it is considered profitable to transport certain materials and physical goods from one system to another, which is why they have a regular trade. Some governors rebel from time to time, blocking "naval routes" which allows for occasional wars. So how big could the terrestrial empire be? How many systems could it occupy? I would like some free systems for political play and space for "Space port" like city states. Can I achieve?
Edit: Door Connection: There are some bottlenecks, but in general they only delay the time it takes to get from point A to point B. A system can alternatively have 3, 4 or only one door. Powers: The only "empire" would be the terrestrial, on the "outskirts of the empire" are some independent states but they are more like outlaws than well-established governments. There are systems without human presence, systems at the end of alleys