If it helps, the word is about 80 years old and was coined by Black musicians in the 1930s, most notably blues legend Lead Belly, who would end concerts by telling people to "stay woke".

So it's not just a contrived way to say "awake"; it comes from natural speech.

Your definition is pretty much the same as the original definition. It means being aware of the existence of systemic racism, and for Black people especially to be aware of the threat that entails.

That definition hasn't really changed. If someone says they're "anti-woke", assume they mean that they don't want people to be aware of systemic racism. Not that they're denying systemic racism exists, but that they want to protect it by reducing awareness of it. You'll find that this definition makes perfect sense in that context, and they're using "woke" to mean the same thing Lead Belly meant in 1938. They're just against it.