You DO see that politics are inevitably tied up in the root cause/purpose of unions though, right? I mean, often it is nakedly political reasons that unions even come to exist in the first place, or this situation with Amazon, for example. Your explanation of what a union is could easily be rewritten for a society made up of constituents electing a candidate drawn from the community to represent them...
What nakedly political reasons do Amazon workers have? They were being told to use a plastic container instead of a bathroom so that they would spend more time working, they were being ordered to put their health and their coworkers' health at risk with inadequate COVID protection, and after more than a year complaining about their working conditions little action was taken (but the workers who complained the loudest were fired for complaining). Amazon management's only response to the effort to unionize in response to all that was to hire consultants to discourage unionization.
Yeah, you are right, the way union representation works is as democratic as political representation. Shareholders also vote on corporate leadership and typically elect other shareholders to the board. That does not make it "political" beyond the internal politics of the organizations involved, and trying to connect those internal politics to the politics involved with government is dishonest.