Yet, politics is not the same thing as managing.
Toxic politics are everywhere, but the ability to negotiate, navigate the organization, find what make people w/ authority tick, is crucial to any successful manager.
Politics is how every organization makes decisions. It's understanding the information flow, the decision making process, people incentives, and how to influence these to get the outcome you want.
Managing up is about altering decisions made above your level (info moving up) and managing down is about taking those decisions made above your level translating them into decisions that affect your team.
i.e. Managing is very much about politics.
Engineering has politics too, just different kind of politics. You also spend a lot less time explicitly doing politics. But, a lot of what is going on in code reviews for example are dominance games and status managing. How you present yourself so that they perceive you as technical the right way matters too.
Make following exercise: how many managers you know are actually spending much time with "helping people solve their problems" or "patiently answering dumb questions"? Managers I know spend some time with it, but frankly, much less then analysts and not much more developers.
Another exercise: Do you know managers that are unpleasant around, arrogant or misinterpreting people? Do you know managers who are actually not good at all at communicating down chain? Because I know a lot.
what the exercises show is that none of that pleasant communicating to all has to do with who is actually successful as manager or selected for management.