There is a role like you're describing at some companies, often called a technical program/project manager. They're responsible for managing schedules, communic

There is a role like you're describing at some companies, often called a technical program/project manager. They're responsible for managing schedules, communication, etc. The difference with a staff engineer is that TPMs are not expected to be technical experts, while a staff/principal engineer is. So they're not just routing information between stakeholders, they're also synthesizing and evaluating, partly responsible for the project going well and empowered to make changes they think necessary. All of that takes a lot of experience in the trenches, having seen many projects succeed and fail. It also requires a lot of trust and respect, which takes experience to cultivate.