When I worked as a director for a large tech company I had some similar questions. Because I joined through an acquisition, I never truly adjusted to the network of managers both above, below and alongside me.

Eventually, about a year after leaving to launch a new startup, I read High Output Management. Suddenly everything made sense. I'd strongly recommend reading it.

Many Bay Area companies are led by people who read this book, and I think you'll gain an understanding of what the mid-level managers worry about in their day to day.