The most "woke" part is a line from Catwoman, and it really makes her seem naive. The themes of the movie honestly seem almost "anti-woke".
For example, a major theme seems to be that we shouldn't be shackled to the wrongdoings of our ancestors, nor should we be punished for them. Another theme is that celebrity/hero worship is a bad thing. Finally, we're presented with the idea that a person can make a terrible mistake and still be a good person, which runs directly against cancel-culture. There even seems to be a message about how strong male figures are important in a child's life, which is just about as far from woke as one can get.
It's a different superhero movie to be sure, but it's not woke. At least not in my eyes. It's a mix of noir detective stuff and more traditional superhero tropes. Think "Seven" meets "The Dark Knight" and you're almost there.
I honestly think people were actively looking for wokeness (and who can blame them?) but that may have made them see woke aspects when, in reality, there really weren't many to be seen.
I was trying to explain why it seems that it is woke and anti-woke at the same time.
The main story arc for Batman is anti-woke, so the core of the movie is anti-woke but they had to infect it with modern day politics so you get a bit of woke mixed with a good story.
This is my conclusion based on comments and the spoiler free review done by Critical Drinker.