The energy derives from gravitational potential energy. The core of a bit more than a solar mass collapses from the size of the Earth to a 10km radius. Some of the gravitational energy (a tiny percentage) released is transferred to the overlying envelope and blasts it into space. Further energisation takes place due to radioactive decay.
A ball of neutrons is not a star-sized nuclear explosion ?
I don't understand what you mean by reaction product? The proto-neutron star consists mainly of neutrons(!) and neutron-rich nuclei.
The collapse occurs because electron degeneracy pressure is circumvented by neutronisation (inverse beta decay), which removes electrons from the gas. At that point, the collapse occurs on a freefall time of $<1$ second. There is no "burn-rate" as such; just a collapse and then a "core bounce" as the equation of state hardens because of neutron degeneracy pressure and the strong nuclear force between closely packed neutrons.
The "observed" energy (i.e. the electromagnetic output and ejecta kinetic energy) is only of order 1% of the energy released from the gravitational collapse. Most of it emerges in the form of unseen neutrinos. So there is no energy gap and plenty of energy to power what is observed.