It's because they commandeer terms.
Woke is the complete opposite. The term gained popularity with the Matrix, Morpheus, and the blue-pill/red-pill scene. It took root in the nascent and started to actually work. The apparatus then commandeered it.
The same thing happened in the 60's with the "counter-culture" movement. What is the root word of culture?
The same thing they were pushing.as counter-culture.
Same thing happens with the term progressive. There is nothing progressive about those policies. Yet they commandeered the term.