I coach new engineering managers and have been both an engineer and a manager in the past. Management is fulfilling in an entirely different way than engineering is fulfilling. It's not only a career change, it's a change in mindset. If you are working as a manager but still living in the engineer's mindset, I can completely understand how it would feel very unfulfilling.

It's not easy to make such a mindset change as an adult but I know it's possible because I've done it and I've seen others do it. It's a very personal change, kind of like breaking out of a psychic prison. It's not something you can think your way through, it's not an engineering problem to solve, it requires a deeper change in your beliefs and in how you use your mind from moment to moment.

Engineering requires extreme internally-focused attention and an intensely analytical mindset and a "deep thinking" approach in order to keep all of the inner models and abstractions clear and well-organized. Management (and especially leadership) requires a practice of broader externally-focused awareness and a more intuitive mindset. A manager needs to hold several perspectives more loosely and have a "wide thinking" approach in order to be a great leader.

All of the "soft skills" are either easy to adopt, or hard to adopt, depending on where your mindset is. If you are the engineer's mindset, you might find it very challenging influencing others or making yourself emotionally available as a leader. You know how people get "developer head" after a long day of coding and have a hard time communicating with people? Developer head inhibits the leadership soft skills. But in the manager's mindset, presence is completely natural, and from a place of presence things like empathy or approachability are natural too.

For me it required 3-4 years of uncomfortable growth, and quite a bit of what I would call spiritual work, before I felt I had really found the manager's mindset.

I hope this is helpful somehow; I'm happy to chat further about it anytime. :D