Not to mention, the signal strength seems too weak and unstructured to be useful as a basis of any higher order machination. A supernova is unlikely to cause much of anything outside of its immediate vicinity. Unlike neural pathways that are highly structured and mostly lossless, radiation disperses out in all directions and weakens with the square of the distance.

Unless there's something big we're missing. Maybe the cores of stars contain the final ingredient required for DNA formation or something.