There is no single overarching government. Some planets have multiple governments while some governments span star clusters. Earth is still a smattering of different governments, although many of those have far reaching colonies. There are empires, republics, oligarchies, tyrannies, anarchies, communes, and many other forms of governance across the various inhabited worlds. Each alien species is also separated into different subcultures and governments.
The galaxy is a crowded, messy place.