[NotAnOtter]

My definition of science is something like "a methodical approach to reach some truth" whereas engineering is something like "a methodical approach to reach some functionality". And I think some version of that is pretty universally accepted.

So by that definition, prompt engineering is much closer to engineering than science. That said, I would consider it closer to product development than either of the above two; I don't count 'tell an llm you'll torture it until your website is hopefully less buggy' a methodical approach.