None of these are actually documented as falsehoods but rather hinge on a deep disagreement about the meaning of the word "woke", so they don't technically meet the definition of lies. Nonetheless, they clarify a profoundly different outlook that is not acknowledged in TaraElla's writing as far as I can see.

For the usage and definition that TaraElla is responding to, it is helpful to understand the history of appropriation of the term. For instance: https://www.nytimes.com/2021/08/17/opinion/woke-politically-correct.html

(Edit, for anyone who doesn't want to read the whole article, the key observation is: "We understand [that rejecting wokeness isn't simply anti-blackness] when we see that the real wind behind its wings in the early 2010s was that “woke” served as a handy, nonpejorative replacement for “politically correct.”" I concur: this is my personal (i.e. anecdotal) experience with the usage of the term.)

Anyway, you make a powerful case, if an arguable one, and in light of that it is not entirely unreasonable that you would view TaraElla's statements as materially false. I think TaraElla speaks well for herself, and I think you have spoken compellingly for your position, so if there are any readers besides us two remaining, I encourage them to think deeply about the arguments presented.