> In other words, what public tech company can engineers work at where you’re not battling for visibility and preference?
There isn't one. Identifying and influencing the people who decide stuff--who does what work, business and technical strategy, your bonus--is always a valuable and necessary skill. A good manager can do some of that for you, but can't take it over entirely.
More practically, variation from group to group within a large company is usually bigger than variation between companies. I doubt a useful answer to your question exists.
If you want a job with less politics, then you're probably better off assessing specific opportunities than assessing massive companies on average. Like, ask "How did you choose the tools for your most recent project?" in the interview, and see what that tells you about their power structure.