For example, in glycolysis, NAD+ is reduced to NADH and then it's more energetic. Why adding electrons to an atom gives it more energy?
While I think you are making the mistake of confusing reactivity, which is more a topic of chemistry, with energy, there could be a reason to presume that an atom with more electrons has more mechanical energy.
Particularly, since $$E=(mc^2)^2+(pc)^2$$ any object or particle of some mass or momentum must have energy. By this rudimentary logic, any atom containing more mass (and electrons have 9.91e-31 kg of it) should have more energy.
But this is a simplistic argument and doesn't explore the other things that happen in exothermic or endothermic reactions. The reason that this particular part of glycolysis is endothermic (gaining energy) has nothing to do with the number of electrons and more to do with chemical laws that don't rear their heads into nuclear or quantum physics topics too directly.
With regard to glycolysis itself, the attachment of a reducing hydride to NAD+ would create the more stable and less reactive NADH, so it only follows that the creation of NAD+ from NADH would create a more reactive product. Reactivity itself is once again a chemical attribute, associated with the tendency of unpaired electrons to create bonds with other molecules.