Why not just let the product manager use some no-code tool?

I think software engineers are having an identity disconnect from their roles as engineers vs coders. Engineering is about solving problems via tools and knowledge through constraints. An engineer is not diminished by having other engineers or better tooling as assistants. If you are having problems understanding your role in the problem, frankly you need to review your skillset and adjust.

You are correct in the abstract, but concretely I contest how useful LLMs are for producing software. I don't doubt their usefulness in prototyping or, say, writing web apps, but I truly do not think they are revolutionary for me, or for software development as a whole.