I'm not sure exactly what the question is here, but I'm comfortable saying that the definition I gave isn't a "later" thing. It's the historical/factual origin story of the word. As with many cultural things, Black folks will often invent something, and then it gets appropriated because it's cool (for better or worse).

What you're saying, if sincere, is extremely late stage. I'm very comfortable with:

It was solely "our" thing for a while, I mean I can recall that usage even before the year 2000. Somewhere MUCH after that it gets a little bit more popular (e.g. either due to or more likely downstream of the Childish Gambino song Redbone?) and (perhaps likely to more white liberal folks using it) begins to "feel" more concrete than before, despite not actually much being so.

And perhaps more importantly, IMHO "the right" is always desperate to find codewords they can use to put down minority groups without obvious slurs. "Woke" fits the bill pretty well, especially since it evokes AAVE.