

Historically it is a term used positively, for example in the expression ‘stay woke’ (1930s). So it is not really a reclamation, but rather a recent relegation by right wing people to a negative connotation. I have however heard some people legitimately use it in a positive manner, and some further reading on the Wikipedia page seems to support that even recently there are political leaders using it in a pro-racial equity sense.
Not really, that theorem says there are true things that cannot be proven, whereas this question is more about running out of proofs that you can make.