I know it's fun to hate on the big tech companies recently and act like they are bullies (and indeed in many ways they are), but this is a bad example of that. Most companies I know of would outright fire you if you, against explicit company policy, went to the press and started badmouthing your employer. The fact that Amazon only gave her a warning is the only surprising thing in this article.
Legal obstacles aside, though, it would be pretty clearly inappropriate in this case. If I'm an entry-level SWE looking to unionize, the principal designers are by any reasonable metric management; they're the ones who go around telling me what I should do and how I should do it, often more so than the person I actually report to in the org chart. I don't think any union representing line employees would let those employees' managers join.