Declining to accept an employee's set of ultimatums, an employee who already engaged in threatening legal action for months and months, is arguably a much clearer framing than "her willingness to assert her rights under the law"
Therefore "recently conspiring a legal battle against Google, while on Google's payroll." is worth sharing, it provides information not present in the limited frame of "her willingness to assert her rights under the law"
This doesn't at all sound like the case. It sounds like the company did something aggressive, she got representation who threatened to sue, and the company backed off, and all of this happened over a year ago and is essentially a closed chapter.
Very credibly threatening to sue your employer with a legal firm, regardless of whether you were in the right to do so, is never a closed chapter. Companies are made of people, and those people are not going to forget something like that. They're going to be waiting for their first chance to get rid of you.
Right or wrong, justified or not, if you threaten your employer with a lawsuit, you need to be looking for a new employer that very same day. The employment relationship is now irrevocably a hostile one.
What you called out as "doesn't at all sound like the case": [1: they continued employing her for months and months] [2: while her lawyer was threatening to sue the company]
First paragraph of the email OP posted, which I am defending as worth sharing: "This happened to me last year. [[1]: there has been 11+ months, or months and months, since this occurred and she continued employment] I was in the middle of a potential lawsuit for which Kat Herller and I hired feminist lawyers who threatened to sue Google [[2]: her lawyer was threatening to sure the company]"
My reading is that the situation you're describing is resolved, and has been for quite a while. Thus no lawyer is currently threatening to sue, nor have they for quite a while.
Thus: an employee asserted her rights under the law in the past, and the situation was, apparently, resolved to everyone's pleasure. "recently conspiring a legal battle against Google" is a misrepresentation of that.
Whether she was overly saber-rattling is, I think, not a meaningful discussion. "How could this ethicist have managed to keep her job" is a straightforward and uninteresting question: don't make any waves, don't challenge anyone too senior, make the company look good in public. "Does Google value talented AI ethicists who are genuinely committed to their work and are willing to sacrifice their career over it" is a much more interesting question.
Google found that there was a credible allegation that Andy Rubin raped another employee, and they figured out how to keep him around for years, until word got out, because he was valuable to the company. (And then they gave him a $90M exit package.) Timnit Gebru got fired while she was on vacation for simply being impolitic. That shows how much Google valued her work.