I used to think this way. Then I became a manager. (Now I'm an individual contributor/IC again.) Oh, how wrong I was.

Managers do coordination, which is far different than building, but typically more valuable. Why is it more valuable? Leverage.

If I as an IC do the wrong thing and it doesn't get to production, it typically wastes my time (and any time needed to fix the mess, if doing so is harder than `git reset`).

If a team of people do the wrong thing, then that's an entire team's time wasted. Managers exist to ensure that a team is pointed in the right direction. Figuring this out could include meetings (oh so many meetings) with other parts of the business or customers, discussing priorities and timelines and ensuring dependencies are understood and met.

You also need to foster intrateam communication so that Bob learns that Alice has already partway solved problem X, or Alice learns that Tracy has experience in technology Y. Sure, you could rely on ICs to do this, and good ones will, but I've seen communication short circuit big issues and save lots of development time.

Is the manager's effort overhead if, by their efforts (even partially, with the help of other team members), the team solves the correct problem, rather than the wrong problem correctly?

This explanation ignores the political aspect of management (protecting your team from budget cuts, layoffs and being pulled into extraneous meetings/other efforts). I've intentionally ignored this because it was minimal at most places I've been a manager, so I can't speak out of personal experience. But I've heard about other places where this was a large chunk of the value added by management.