So we take 2 bar magnets confine them in a plastic "c" section channel perfectly flat note they have 0 kinetic energy and some potential energy relative to there hieight from centre of earth it doesnt matter. Now we slowly move them closer micron by micron at some point they attract and fly together. You hear the click of noise and they moved so there is energy transfer. After the join they still have zero kinetic and the same potential energy. The classic school answer is there is no energy in a magnetic process but you can see that isn't strictly true we lie to the students. So now the question where does the energy come from? I will leave you to ponder that one and perhaps do some reading.
As you say you can ignore the gravitational potential energy, because we are looking at a system that is all at the same level and gravity has no direct effect.
Now there is a potential energy present that has to be taken into account. That is the magnetic potential energy between the 2 magnets. As long as they are separated this potential exists. And it causes the 2 magnets to be attracted to one another.
Your description of the experiment leaves out one thing that is influenced by gravity. That is the friction that exists between the magnets and the surface of the channel. Gravity keeps the magnets in contact with the surface under them and produces the friction. This is why the magnets don't move toward each other until they are a certain distance apart. When the attractive force between the 2 magnets is large enough to overcome the effect of friction they begin to move toward each other.
As the magnets gain speed they gain kinetic energy. When they meet the kinetic energy is released as sound (the click you hear) and heat. At that point it is true the magnets will contain no kinetic energy and no potential energy with respect to each other, but the energy doesn't just up and disappear, it is transformed into a different form. The kinetic energy of the magnets is transferred to the molecules of air and the material the magnets are made of. Of course some of the energy will be transferred to the surface the magnets are moving on, which will be heated by the friction.
I'm not sure where you get the idea that schools teach there is no energy in a magnetic process. Magnetic processes are used to generate power, to change voltage levels in power transmission systems, and to turn motors, among many other things. There are some theoretical (idealized)discussions where things can be moved through a path which results in no net energy change. Of course in these discussions there are instantaneous changes in energy levels, but the overall result is that all the energy transferred between different parts of the system is returned to its source at the end.
Bill Gill
