I thought it followed the Socrates tradition in that the true philosopher is the one asking the questions, and it is the role of the student to answer them.
I wish I remembered who I am quoting here
The split of art vs. design you're talking about or one of the many ways to divide the act of creation into a classical/romantic divide or one of the many other ways to describe it should be considered harmful.
And I'm not trying to split hairs here but wishing the dichotomy you're talking about didn't exist and encouraging folks not to frame the world that way.
If we think of Leonardo da Vinci he created both art that created problems, and inventions that solved problems. But these world where very separate.
If you have an idea that there's a split between "creating beautiful stuff" and "creating useful stuff" then your world turns into one where something is only one or the other where someone creating only does one or the other.
These days it's thought of unique or special if something is both and the fact this isn't standard is influenced by the mental model of them being separate.
Human progress depends on both: defining the problem and solving it.
You can draw images in the sand. Is a stick "technology"? What about using your finger?
Do we need paints? There are natural dyes. I don't mean in the sense of extracting things but some are as simple as "smash this berry". I believe the answer to this is rather critical since you specifically mention cave paintings. Many of those were done by hand, not by brush.
What about things like rock balancing? Sand sculptures? Singing/vocal instruments? Poetry (spoken, not written)? Story telling (ditto)? And so on
There is so much we consider art that can be done by any human with no tool use nor any external objects. I won't even mention how people call a sunset a work of art, and I do think we should avoid that as it has the same problem I bring up with defining technology. But I do not think most people would consider speech or vocal sounds technology, though certainly we would include things like writing.
It takes a considerable amount of development before you can make the distinction at all between separate concepts of art and technology. For a long time there wasn't a split because it was difficult to conceptualize how to split the two.