Interesting. I'd define all of those tasks as the job of a team/tech lead, rather than a manager. I've worked at places where the same person did both roles, and it was not always a great mix.
People management is about managing the company's resources to achieve goals. If you are not the one leading the implementation of those goals, you are not going to be able to:
* reason about what the right about of resources should be
* see opportunities for optimization
* forecast future need
But the thing is this makes no sense. Tech issues always turn into people issues - when there is a disagreement, who adjudicates? How can a manager adjudicate something they don't understand. And how will engineers respect / follow the decision?
And people issues invariably become tech issues. How can you hire the right people if you don't understand the tech? How will you know when to fire?
This setup makes no sense to me and i have very rarely seen it work. It seems like it was a product of an earlier time when there was a lot of money floating around and provided a way to (a) shield senior eng from dealing with people problem they just didn't want to, and (b) provide cushy jobs to professional managers that didn't know much about the tech.
But it doesn't work. There's no way to do the shielding well and a person with hiring/firing power needs to know what the fuck is going on.
Really good eng leaders must be both good at tech and good at people. That's the job.