Management is where engineers stop growing. Managers aren't regularly cultivating new skills as engineers are.
Of course you grow as a manager. But you're right you're not growing as a technical expert - that's not the goal of managing. Managing becomes more about the business and less about the technical details.
It's a very different job and an important one if you know anything about running a larger company. The technical work you do as a IC is one part of many that drives the business forward.
As an engineer it's easy to practice many new skills and also to see improvement. I might be interested in orchestration, I pick up Kubernetes course. I want to build iOS app, I start learning Swift. After a month or two I can see a difference in my skills. Others can see it too - I contributed to iOS app at work which I haven't done before, it's a new skill I learned.
As a manager, I need to be better at negotiating with stakeholders, or recognizing underperformance, or interviewing candidates. I can read books, take courses, but I can only see my improvement over longer period of time. What's more, most of people around me won't see that I'm a better interviewer now, or that I'm better at helping to improve individual performance. It doesn't mean I stopped growing, it doesn't mean I don't cultivate new skills. They're just different skills.