That's not really how it went. You'd only think that if you were asleep.

There's a segment of the progressive left that isn't particularly liberal--you need to think and say the right things, their things (only), and they'll attack you very vocally if you have any other ideas, explaining that free speech doesn't mean freedom from consequences. (And oh boy, are you in for a LOT of consequences!)

But they won't say who they are; they won't identify themselves as a group.

How do you talk about them, then?

Well, you wait until they talk about each other. And one thing that they picked up and said to each other with admiration was that they were "woke".

And the community who pioneered the use of the word didn't say, "Hey! Use your own word! That's cultural appropriation!"

"Woke" didn't get the attention of whiteness. Illiberal leftism got the attention of everyone. The initial reaction was mostly from liberal leftists of various stripes who, despite their unease with going against the illiberal leftists' strident proclamations of virtue, thought that power relations between identity groups was maybe only part of the story, did think that maybe free speech was getting pretty short shrift, maybe respect for individuality was getting trampled on a bit hard, that maybe this wasn't the wisest plan: (1) deconstruct every part of society and culture, (2) ???, (3) justice!!!

The unnamed but same-thinking illiberal leftists attacked back, charging the liberals with all sorts of horrid moral degeneracy of the type that usually only gets leveled at the right (not infrequently with good reason). Perceptive liberals started to view "woke" as synonymous with "illiberal bigot with delusions of saintly morality". That's when it started accruing negative connotations.

Only later, after burning through "Social Justice Warrior" and, very briefly, "Critical Race Theory", the right was all--the enemy of my enemy is my friend, amiright? Let's call ourselves anti-woke! We'll get some of those other anti-woke people on our side, and have more power!

Now practically all you can hear is the right's propaganda machine bashing everything as woke: their own fantasy of what isn't even happening, what is happening and is a bad idea, what is happening and is a good idea but which they oppose, etc.--all woke, all mocked, all exaggerated.

The key place where the term was hijacked, though, was when the illiberal left was allowed to use it without pushback. Ostensibly they were the strongest allies of the black community--a fair number were part of the black community--but because a word was so sorely needed to describe that illiberal leftist strain of thought, once "woke" was in wider use, it was guaranteed to get away because a label was needed. But a lot of illiberal leftist thought isn't love, it's hatred. Hatred in the garb of love, often enough, but hatred nonetheless.