Nice try, and I understand where you're coming from. Unfortunately, you're a tad late. 'Woke' now simply means a bunch of white middle-class poseurs who scream and shout when somebody uses a word or offers and opinion they don't like. They aren't even consistent - a man will get harassed or even cancelled for denigrating women, unless he happens to be a Muslim, in which case his 'minority cultural values' are to be respected despite their clear misogyny and sexism.

Woke people are the ones who go for the low-hanging fruit. Idiots like J K Rowling or Prince Andrew, for instance. But one thing they do NOT do is make any serious effort to change things. Most of them are quite comfortably off, thank you so very much, and have no intention of removing the system that made and keeps them so. Let's just virtue-signal and attack people who use the wrong words instead.

The word for people who are ' aware of societal injustices and oppression and how various institutions interact and prop up these forms of oppression'- and who are actually trying to change those things- is the same as it has always been - Socialist!