My job is exactly like what you describe. In a way, I am the executive branch of management. I don't decide what needs to be done or how it needs to be done. I just make sure it gets done.

I pair people with questions with people with answers. I synthesise business requirements into usable tickets. I take ownership of cross-team tasks to make sure they don't get stuck. I digest a lot of information, and share the relevant bits with the relevant people. I make sure that important conversations happen, and that important things aren't forgotten.

In other words, I take care of all the details that would prevent the team from being focused and productive.

It's pretty fun. I am told to make things smoother, but left to decide how to do it.