I disagree with your view. It’s the thinking needed that makes it engineering, especially when you have a lot of constraints (massive scale, low latency, etc.).
Consider this: math is mostly doodling some glyphs on paper, so clearly it is closer to drawing than engineering.
To be fair most actual engineers just copy paste from a previous project (MEP engineers in architecture) or just look up numbers or equipment in a table (every structural engineer I’ve known). A vanishingly small percentage of any engineer (software or otherwise) are actually doing what most people think as “engineering”.
Consider this: math is mostly doodling some glyphs on paper, so clearly it is closer to drawing than engineering.