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The potential energy of the spring is “stored” in individual molecules that are pushed into some configuration that they don’t quite want to be in, and they exert force on each other trying to push themselves back apart / back together into being the way they like. As the spring disintegrates, you could model those individual forces, and molecules exerting force on each other would release it into kinetic energy one by one or in groups, as the spring gradually lost its integrity to exist as a singular entity.
(I think that in practice, metals are made of grains, big groupings of molecules which stay pretty much as rigid bodies unless something really crazy happens, so most of the potential energy is force of the grains wanting to go back into their preferred arrangement in relation to other grains. I.e. not in practice at the level of molecule to molecule. But I’m not 100% on that part.)