MLOps is deploying, monitoring and (re)training ML models. Sits in the DevOps and data engineering space.

Prompt engineering is making generative AI do what you want by crafting the right context. I would put it somewhere in the software and data engineering space, given they will most likely integrate applications with it. MLOps comes into play if you have your own trained or tuned model.

More of a thing, but it's mostly DevOps.