Abyseusseus is not an example of a Planet-State since it is the homeplanet of another Empire, it contains a nation that functions like a Planet-State.
A Planet-State is a planet controlled by a Race of any kind and does not have an influence to another controlled planet of the same race. In general, these kinds of Empires function like a city-state(the Greek Poleis/city-states to be exact). A good modern-day example of Planet-States is the Paraty Urekies(planet-states in Paraty Language). The Paraty Urekies used to be one Empire until the Spodum Empire Collapsed, then it turned into self-governed planet-states with different types of governments.
Think of a race in the civilization stage and they have spaceships(at least 10). You just thought of a Planet-State