I don't think that's what woke means.
Woke to me in the simplest sense if a form of extreme egalitarianism, collectivism with some blank-slatism.
Let's take your example: poor and Black people don't live on LI with equal representations based on other groups. Let's unpack that:
1. You have some definition of "Black" that's very broad. What does someone from Sub-Saharan Africa whose ancestors came here on a slave boat have to do with a 0 generation Nigerian immigrant who is significantly better off than the median American? Then you have the whole "Brown" category which is equally ham-fisted.
2. Ignoring any differences in group preference and autonomy. There could be no reason that the proportion of said group would be unequal in that area if not for some force outside of their control. You ask why aren't there enough of [group] in some extremely competitive professional field, but you don't work backwards. For instance, federal judges -> prestigious law school graduates -> prestigious undergrad graduates -> high school graduates -> parents in home. Woke ignores the chain and usually just jumps to the end result. Of course this is ignored in some domains. No one argues that prisons are overly harsh (lenient) on men (women) when it comes to criminal punishments relative to each other. Or why are there so many central / South Americans in MLB. It's uncritical.
3. Groups are the organizing force (collective guilt). [Oppressor] group did this to [oppressed group] so we need to change the balance of power of [oppressed group] in relation to [oppressed group], when in reality there are only individuals.
Overall, things are simplified to oppressed vs oppressor. It's an oversimplification and leads to bad things like shutting down accelerated math programs because we don't like the makeup of the student body