I see no objective definition but lots of subjective claims. Subjective terms are inherently meaningless. I have seen people scream "woke" merely for supporting equality of rights for gay couples. They scream "woke" when parents help their trans children. I've seen people denounce as "woke" the denuciation of anti-Semitism. It is used so widely because it describes the subjective feelings of the one shouting the term, and it has no clear meaning that we can define. In fact, I have never seen it defined.

You say, "It's the mob run amok." So are you saying the mob that violently attacked the Capitol are "woke right-wingers"? Or are the exempt and only those who protest police violence are woke?

The protests of police killings which were denounced as woke were far more peaceful than the January 6 mob but I've never heard woke applied to them.