I’ve been an engineering manager myself for the last 10 years and one thing I have also found is that I still like doing hands on stuff. You have to manage your own motivation, not just that of your team(s), regardless of what the “ideal way” to spend your time looks like in your environment.

Sure as a manager you have to plan, communicate, go to meetings, handle conflicts, prioritize tasks and so on. When all is said and done, keeping a slice of time doing what originally got you in the engineering business in the first place, might be just the thing that keeps you going.