Yes, context matters. The greatest painting in the world is just crushed materials smeared on a canvas, it's nothing too special without the context.
A computer (not even an LLM, just something generating random pixels) could randomly generate the exact same pixel pattern as the greatest painting in the world, and it would not be the greatest painting in the world, because context matters.
Because of what?
Context.
Is it the lack of hate? I could put all the hate I have into a person or group I hate while composing an AI art piece for instance.
No you couldn't, because you can't compose AI art. The AI composes it, and it can't feel hate.
I don't paint physically with paint when I use photoshop either. Photoshop doesn't feel hate.
The sentience of AI is also an open question.