Political correctness and language codes are not new. I think what was new is the idea that people could rally around the banner of awareness, and thereby avoid disputes about solutions. This is why many of these topics lose momentum once their followers get the attention and have to deal with the hard and less popular questions of how to fix something.
I think what most people call "woke" is probably just a reaction to the obvious emptiness of many of the things politicians like Kamala Harris chose to focus on whilst ignoring more concrete issues. A lot of it was stuff there never was a solution for.
Put another way: the culture war (as woke vs. anti-woke) divides the electorate, but in a way that lets them be parceled out between two factions of the ruling class, rather than aligning any of them against the ruling class.
The idea that wokeness is in contrast to class-based advocacy is not correct. The right will happily call class-based advocacy "woke" until the cows come home.