When it comes to interstellar empires, we could classify them by how much they deal with planetary governments.
Distant empires don't interfere with local matters at all - sort of like the relationship between the US Congress and the town council of some place out in the middle of Wyoming. All the empire cares about is that the taxes come in and the planet doesn't rebel. The Third Imperium is a Distant empire in some interpretations.
Close empires usually leave local affairs to the locals, but the imperial representatives might actively advise, mandate, or interfere. Usually there are some minimum legal requirements that the locals have to adhere to, such as sapient rights and the like. In other interpretations, the 3I is a Close Empire. Star Treks' Federation is (presumably) a Close Empire as well.
Integrated empires build the government from the planetary level up, so all worlds are active participants in interstellar affairs. Law level (in terms of crimes and banned goods) is effectively the same across all worlds, but enforcement might vary. Tech boosts to a minimum TL would be common, as would planetary specialization (focus on a small subset of potential local production). Imperial representatives are in fact the representatives of their world's to the next higher level of government. Treaty alliances fall into this category.
Commanding empires impose governmental order from the top down, and are usually semi-centralized. Local needs might be taken into consideration by the imperial representatives, who are the rulers of their worlds.
Shipyards shouldn't be that common. On demand construction could be very common, but a dedicated shipyard facility requires a constant stream of orders to keep running in addition to making up the huge infrastructure costs. A port with no shipyard could construct a ship using just the capabilities of its repair shops, but work would be much slower and possibly more costly. Maybe throw 8+ for a dedicated shipyard of the indicated level, with a +2 for each level below? And -2 for each level above? Imagine Class C berthing facilities with a Class A shipyard!
What if we started a project to create subsectors, preferably not set in the OTU, and put them online for new referees to grab and start playing? 40 years of canon (even if mongoose hasn't been putting out original stuff) is a lot, and there's always that one player who will read up on everything to get an advantage over the referee (they usually find the refs who won't stand up and change things). Minimal canon semi-blank slates just might be a popular thing...
Any government type can go with another type! Consider an empire where the planets are mandated to have a representative democracy: rather than the same government between worlds, the government roll shows how that democracy is implemented (or corrupted) on the different worlds.