I'm not sure I understand your question. Πόλις is not a word that refers to any type of government. Πόλις is simply the word for a city. Specifically it is often conceived of as a self-governing city, as opposed to ἄστυ, a city or town that is governed by another city, but the distinction is not necessarily drawn--the Athenians often called Athens "τὸ Ἄστυ," in the same way that the Romans called Rome simply urbs. The two words can appear together, in which case ἄστυ means the physical city and πόλις usually means the citizen body and by association whatever state institutions exist, but even that's not really a hard line since πόλις was also used to refer specifically to all the homes of the citizen body. There's nothing in the word πόλις that describes a system of government, and a πόλις can suffer from στάσις just fine. I don't think I really understand

"State" is the worst word to use for this comparison because it's a specifically post-enlightenment western word which connotates institutions, sovereignty, and recognition. The word in its western (including English) incarnations maps very very poorly to both Greek and Chinese concepts.

Simultaneously, you're picking the wrong pairs for comparison.

If you really want to compare, you should match up πόλις with 成 (chéng). That way, you're at least talking about a localized socio-politico-economic community usually bounded in some capacity by its city walls.

I'm not even going to get into the clusterfuck of trying to pair up πολιτεία and 國 because then you'll have two thousand years of western theory trying to unpack "res publica" from "state" which we use to interpret all other entities approximating that word.