During core collapse energy liberation, what percentage of the $10^{46}$ joules is carried away by neutrinos?

Over 99%

The gravitational collapse of the massive stellar core converts a staggering amount of binding energy into other forms of energy, quantified as about $10^{46}$ joules. The mechanism for carrying away the overwhelming majority of this energy is the release of neutrinos, which are weakly interacting particles generated profusely during electron capture. The text explicitly states that over 99% of this liberated binding energy is carried away by this torrent of neutrinos. This massive energy outflow explains why neutrinos are the prime candidates for re-energizing the stalled shock wave; although they carry away the energy, depositing even a tiny fraction of it back into the shock region is enough to potentially power the explosive ejection of the star's outer layers.