No, I really don't think that prompt engineering is the same thing. Anything I put in the prompt may help this particular conversation, but a fresh instance of the LLM will be exactly the way it was before I started. Improvements in the LLM will happen because the LLM vendor releases a new model, not because I "taught" it anything.
Yeah. I do agree with lovich that there's a lot of stuff about management that's just not fun (and that's part of why I've always carefully avoided it!) -- and one thing about AI is not just that it's management but that it's management with a lot of the human-interaction, mentoring, etc upsides removed.