I think you've done well laying out what a lot of people want "AI Engineer" to mean at this moment in time. My concern (coming fresh out of the absolute semantic nightmare that was the "serverless" community) is that the term AI is so hopelessly overloaded, and has been such a moving target over the years, that it's unlikely that a plurality of people will ever share your mental model of what an "AI Engineer" is/ does / knows / is paid.
Personally I've been using Generative Engineering / GenEng [0] to describe the professional practice of building stuff with AI as your pair programmer. I recognize some are pulling away from the term "generative", but to me it feels like a better anchor into the specific flavor of AI we're talking about.
[0] https://cloud.google.com/blog/products/ai-machine-learning/t...