I don’t think civility has a lot to with civilization in the anthropological sense of the word.

"...first use in English is attributed to Adam Ferguson, who in his 1767 Essay on the History of Civil Society wrote, "Not only the individual advances from infancy to manhood but the species itself from rudeness to civilisation".[14] The word was therefore opposed to barbarism or rudeness, in the active pursuit of progress characteristic of the Age of Enlightenment." [0]

[0]https://en.wikipedia.org/wiki/Civilization

“... in the anthropological sense of the word.” -me, just recently.

If you are wondering where we might find a definition matching that sense, try the first sentence of the article you linked:

“A civilization (or civilisation) is any complex society characterized by urban development, social stratification, a form of government and symbolic systems of communication such as writing.”