The actual meaning of "wokeness" is that it has several different meanings. For instancee, the first could be what you outlined:

1. an "awareness of the existence of social injustice"

And another, equally valid one (that comes about from the reaction to people who embraced the first meaning and proceeded to behave obnoxiously and gain lots of attention) is:

2. the obnoxious and doctrinaire enforcement of the values of the "social justice" subculture on the wider population through bullying tactics (e.g. social media pile ons)

etc.

Taking one as the "one true meaning" is almost always just a tactic to delegitimize an opponent (usually by the left, as they have more access prestigious institutions, but language is language and no authority can suppress new words and new senses of existing words).