Look at your experience in the worst possible way - because that is how hiring companies may see you. You stopped coding, so your are rusty at best. You haven't had a job in 4-5 years. You have no actual managerial experience. So to hire you as a manager, they basically would be giving someone with 5 years of rust on them a shot at doing a job they have never done. That is why they are giving the jobs to other people.

I know that take on your history is unfair. But the question you need to answer is how to fix that perception? Did you lead people when freelancing? Did you manage budgets and payroll? Were you accountable for business results? If so, show those things in your resume.

So what is your understanding of the role and your motivation becoming a manager?

Your remarks are kind of vague. Manager means dealing with people. Have you been in a formal team lead position before?

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.

You probably should set your sights more on becoming a lead developer, where your experience as an engineer will be respected but you can transition into management later on. Also focus on discussing your mentoring experience a lot, including the outcomes you've helped achieve (ex. 200% growth in X, 50% fewer bugs in Y, etc.)

As someone who hires for this role, I look for people who can handle teams well and deliver outcomes, not just code. This means I need to be able to trust you with the careers of the team and the project results.

A good transition is actually consulting on tech teams, which is somewhat a leadership role that will give you the management experience needed later on. More often that not, companies absorb good consultants if they jive well with the team.

It might be easier to start by applying to companies looking for "tech leads" and let them know you're interested in managing the team immediately or shortly. This is how I got into my first manager position.