Exactly what does a network engineering manager do, and how do I get there?

Hey folks,

I've reported to a network engineering manager in the past and thought I knew what he did, but I'll post a bit about what I do in my job currently and hopefully will get some solid advice from you all.

Just to begin, I do have a bachelor's degree, a CCNP and a slew of a million other certifications (including project management) and have been doing strictly network engineering for 6 years.

When I began here, there was only one infrastructure team of the four of us. We're up to 10 now, split up into teams and reporting to a director. However, the person being reported to is much more involved with the server/storage design/expansion/etc, while I take care of everything on the networking side (with the help of my junior guy and security guy of course).

So, I design the network infrastructure, including the new core design we are implementing in our two data centers, plus designing our third data center. I take care of Cisco support renewal, Meraki licensing, managed services contract renewal and maintenance, low voltage vendor procuring, WAN and private fiber circuit procuring, equipment ordering and pricing negotiations, pretty much whatever you can think of. I bring in vendors to discuss new designs and partnerships, and pretty much serve as the point of contact for many of these companies with our company.

Really though, no one has ever told me to even do anything, I just always identified what needed to happen and did it. It has been acknowledged by management that this is the case too, but I am not sure what else a network engineering manager would be doing? I am working on soft skills and attend a weekly leadership meetup, and have been reading books too. I do get advised to delegate work out a bit and lay out the vision, and have been given some opportunities to lead projects which were successful. I have also vocalized my desire to move into a leadership role, but there is just no network engineering department here. I would like to understand from everyone here what else I could be doing to get to where I want to be. This company has 2500 employees and 25-30 locations, so we are decently sized and do a billion dollars in revenue a year. I know the technical work stands for itself (we've also put our entire branch office infrastructure into ansible and our core switches into ansible too, which fits the DevOps narrative around here) but at 93k/year in a major city, I'm starting to feel underpaid and also underappreciated, with no real path forward. I would like to make it work here though but I am just so lost. I threw out some feelers on some high end networking jobs that paid a good bit more, but none seemed to put me closer to management than the job I am in right now.

Can you all help me out a bit?