Major public organizations and interest groups (such as the EFF, ACLU or AARP) that are independent from the state:
Civil society can be understood as the "third sector" of society, distinct from government and business, and including the family and the private sphere. By other authors, civil society is used in the sense of 1) the aggregate of non-governmental organizations and institutions that advance the interests and will of citizens or 2) individuals and organizations in a society which are independent of the government.
I believe Wikipedia has a good overview, in particular "the aggregate of non-governmental organizations and institutions that advance the interests and will of citizens" is probably the definition that best matches the one used in the article.
"Civil society" implies the existence of uncivil people; it's good guys vs bad guys, not civilian vs military. If Ukraine targeted civilian organizations in Russia, the headline wouldn't call it an attack on "civil society" (but Russian media might.)
> "Civil society" implies the existence of uncivil people
It does not. You are conflating:
civil 2b: adequate in courtesy and politeness : MANNERLY
with
civil 4: of, relating to, or involving the general public, their activities, needs, or ways, or civic affairs as distinguished from special (such as military or religious) affairs
You're being naive. Propaganda often employs double meanings, subtext and implications. This kind of language would not be used if the actors were reversed.