Democrats, progressive activists, whoever.
There are segments of the socialist left who traffic in parts of the identity synthesis and segments of the liberal Democratic left who do so.
There is often a conflation between the materialist socialist left and the identity focused left. There is overlap, but these are distinct camps.
I don’t like using the term woke because it’s little more than a right-wing cudgel at this point, but I think a good definition of wokeness is social justice politics with class removed. This is how the liberal identity focused segments of the Democratic Party were able to wield this strain of progressivism against Bernie in 2016.
To say that Democrats haven’t engaged at all in this kind of language is just wrong. They moved away from it a bit in 2024, but the damage had already been done.