What's most confusing about "woke" is to what degree those who might be described as such are willing to own the term. Its origin was genuine afaik, but its stupid past-tense conjugation meant it was more easily used in a derogatory way. Some people still seem to use it about themselves, and that may be gaining in popularity over time. It's become a very common derogatory label for people who are at the very least unwilling to agree with the blob of collectivist-oriented groupthink.
And yes you're right that it mostly applies to identity politics. In fact the phenomenon tries to absorb as many issues as it can into identity politics. The more divisive it can make things, the better its chances of survival. It's almost like an autonomous consciousness distributed among people who subscribe.
Languages are living things... words sometimes get re-worked into ways we don't like, but there are no effective ways of protecting languages from changing.
What woke means today, more so in the context of our current political climate is a far cry from what it meant when it began being used by the Populus. And I suspect it will change again.
Debating definitions however, is a sure way of not getting any systematic change done. It's like arguing about what are the best cables to use for to plug guitars but never strumming a single chord, all while calling ourselves respected musicians.