From what I've been able to gather, the road to where we are now with the word has a few more steps. I can't claim complete accuracy with this timeline - it's just based on what I've observed as a Canadian looking at the American political and pop culture scene from the outside.
It was co-opted at one point by the activist left and for a while came to refer to anybody who was ware of social issues, rather than just those in a particular group (such as the African-American community). The meaning was still fairly benign at that point. But, there were two moments that seemed to really radicalize the two sides of the political aisle, and those were the election of Barrack Obama for the American right, and the election of Donald Trump for the American left.
I think it would be wrong to depict these as inciting incidents. The real inciting incident, as far as I can tell, was the 2008 Financial Crisis. What seemed to happen after that was that the discontent with the system manifested in a radicalization on the right (mainly the Tea Party) along with pushback forcing the other side farther left, and then the election of Donald Trump just pushed the left the rest of the way. And, by the time Trump was elected, this had started manifesting in a full blown culture war. I've spent a lot of my career covering pop culture, and there was a distinct increase in hostility after 2008.
(And even Donald Trump really seemed to me to be more of a molotov cocktail thrown at Washington than an actual serious attempt to elect a workable president. Watching the Republican primaries was FASCINATING - the Republicans did NOT want that man as their candidate, and I remember a couple of articles about the RNC considering changing their primaries rules so that Trump wouldn't win. This was a massive populist "F--- you!" sent to the people in power.)
So, there has been this entrenchment of the two sides that I've seen over the last 14 years, and the way this has manifested on the activist left (and I am using this term to differentiate it from the rest of the left) has been this tendency towards championing things like diversity in a way that is reductionist to the point of absurdity (all black people = victims, all white people = oppressors, etc.) frequently not associated with any actual concrete action, and attempting to silence anybody who dissents (which is now known as cancel culture). The word "woke" has come to be associated with this.
(The far right is pretty nuts too, just in case anybody is worried that I'm picking sides, but the question is the development of the word "woke" into the negative connotations that it has right now, which means talking about what happened on the far left.)
Speaking personally, I gave up on serious pop culture commentary a couple of years ago because of the toxicity. I'd been involved in it to some degree or another since 2000, when I wrote one of the first online video games issues columns in the English language. There was a time when a female Counterstrike player came out and talked about her experience with sexism in the online community, and the general reaction from the community could be summarized as "I had no idea - thank you for sharing this!" That is unimaginable today. I don't actually know if a true marketplace of ideas in the discourse is possible anymore - nobody seems to want to build bridges. Back during the "Puppy wars" I saw members of the supposedly morally upright science fiction community making unironic voter suppression comments that would have been on the wrong side of the civil rights struggle - it was horrifying.
The thing is that OUTSIDE of the discourse, most of the actual population are not members of the far left or far right - they're moderates. One can only hope that one day they regain their voice, but there's a lot of fear out there of cancellation, which I think is one of the reasons this has gone on as long and gotten as bad as it has.
So, sorry to be a downer, but that's what I saw looking in from Canada as a centrist.