Well, then, there you go: that's the meaning of the word, then. Or at least it certainly is to a lot of people.
I think we again don't much disagree, other than in a very surface level about the words. I go out for a beer with some Norwegians, and they self-describe to me as having ideals they call "socialist", because they're ideals around being social and building a society together, and that's what the word means to them. I accept this definition. Maybe you've got a different one in mind; words are tricky like that.
I similarly don't know what to tell you about the utility of taking the precise wording of websites as the ultimate truth of anything. Did every person in every klimastreik around the world read those two websites and sign off total agreement on every detail they proclaimed? Probably not.
I offered anecdata that many people on the ground, even around those causes, are very positive to carbon taxes or other forms of market-aware schemes to make a difference. It is, of course, anecdata. You can take it as a note of hope, perhaps? Or, not. Up to you.