No, that would cost more energy than we extracted from it. However, what we call “spent fuel” isn’t fully used up. It can no longer be used in a normal reactor, but reactors can be build which can continue extracting energy from it. In fact, only about 2% of the usable energy has been extracted from the fuel by the time we start calling it waste. Most of the high–level waste from today’s reactors is really just fuel for reactors that we haven’t built yet, due to over–regulation.

this is fascinating and unexpected. Do you have more literature on this ?

Breeder reactor: https://en.m.wikipedia.org/wiki/Breeder_reactor Not an expert but from what I read development stopped mainly due to uranium supply being sufficient making expensive further research not worth it. But on the security part using liquid sodium certainly contributed :).

In principle, this might be possible since any reaction can in principle be run in reverse, given a sufficient supply of energy.

In practice, I don't think this would be at all viable, and certainly would not be competitive with other much more straightforward forms of energy storage.

It's an operation cycle of very specific reactors, if I remember right its a variation of breeder reactors.

Breeders don't reverse the nuclear reactions that take place when a reactor is producing power. They use the neutron flux from those reactions to induce different reactions (involving much less energy per nucleus) in surrounding material that produce fissile isotopes in that material.

Breeder reactors work by having less useful elements capture neutrons and turn into more useful elements.

Capturing all of the fission byproducts and reversing the process is going to be so technically difficult and energy costly that, in this context, it might as well be impossible.