As for motivation, I think "I feel like I am “done” with fulltime hands on coding" was clear enough. As for understanding of the role, unless the OP's experience is unique then managers are typically former programmers with little to no "real" management training or experience. I realize that's a broad generalization but in my career it's been pretty accurate. Even when managers had training it was usually someone who went to night classes for an MBA and was never that into coding in the first place.

I know I have looked into (but did not pursue) software management because it seemed like a place to "fail up" from being a burned out programmer... I might be the exception in that respect though.