How it's built vs what it looks like.

That's arguably a very limited view of design. Design is far more than aesthetics.

Design is visual engineering .. development is software engineering.

Both essentially involve solving problems.

I don't think this agrees with how the term is used. I've never heard of anyone being said to design a painting or a sculpture. Meanwhile, engineers are said to design things that aren't visible, such as algorithms or a circuits.

We're talking about web design.

If we consider art .. sculpture and painting do require planning, preparatory sketches or a maquette. Design thinking allows us to build and solve.

I don't see any obvious reason why design should come to mean pure aesthetics in this particular domain, and even if we do, what word is left to mean actual design work in the traditional sense of the word?

It doesn't mean pure aesthetics .. the way something looks affects it's affordance.