I look at this contrast as what I call the difference between a "programmer" and a "software engineer". These jobs are really two different universes in practice, so you're not wrong.
I saw an LLM demo at one point where it was asked to write FFT and add unit tests for it which really drove this point home for me.
A programmer is a nicer term for a code monkey. You ask them to write FFT and they'll code it. All problems can be solved with mode code. They can edit code, but on the whole it's more just to add more code. LLMs are actually pretty good at this job, in my experience. And this job is important, not all tasks can be engineered thoroughly. But this job has its scaling limits.
A software engineer is not about coding per se, it's about designing software. It's all about designing the right code, not more code. Work smarter, not harder, for scale. You ask them to write FFT and they'll find a way to depend on it from a common implementation so they don't have to maintain an independent implementation. I've personally found LLMs very bad at this type of work, the same way you and others relying to you describe it. (Ok, maybe FFT is overly simple, I'm sure an LLM can import that for you. But you get the idea.) LLMs have statistical confidence, not intellectual confidence. But software engineering generally works with code too complex for pure statistical confidence.
No offense to the LLM fans here, but I strongly suspect most of them are closer to the programmer category of work. An important job, but one more easily automated away by LLMs (or better software engineering long-term). And we can see this by how a lot of programming has been outsourced for decades to cheap labor in third-world countries: it's a simpler type of job. That plus the people biased because their jobs and egos depend on LLMs succeeding.