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.
Some people are actually registered with an union but their challenge is to have people vote for them during compulsory elections for work councils.
Any employee can vite, and any employee can join a union. The mere fact of joining the union does not protect you form being fired (which by itself is very complicated in Europe where there are strong labour laws). The only people who are strongly protected are the ones who create a union, or are elected as a representative.