>When this electromagnet is charged, it is magnetic, and when you attach an iron bar across the poles of this electromagnet, it will not lose its energy.

Yes it will. The magnetic field generated by the electric current will collapse, but to whatever extent the iron bar was magnetized there will be some remaining. It can no longer be considered energy, however, it's just a magnet.

>The iron bar is shown by fedora guy (another YouTuber idk what his handle is) to last at least 2 years,

Sure. Permanent magnets are just that, permanent.

>and when an LED is connected across both poles, when the iron bar is pulled off, it both loses its magnetic charge and lights up the LED momentarily.

This is no mystery. That is the basic principle of a generator. Apply a changing magnetic field to a conductor, and electrical current is produced. Since you are removing a permanent magnet from an iron core, you are suddenly lowering the magnetic field from the conductor's vicinity.

If it loses any magnetism(it won't lose all of it), it's due to hysteresis loss. This is to be expected with soft iron which easily gets both magnetized and demagnetized. It's a real headache in transformers.

>There is a discharge of magnetic energy. The energy goes somewhere.

No, there is not. There is a conversion from the kinetic energy(removing the iron bar), into magnetic energy(suddenly changing the flux), into electrical energy(as the field has nothing to sustain it, it is "absorbed" into the conductors), and finally a sheer inefficient loss of potential energy as the fragile magnetizing of the iron bar goes down. That is lost as minor heat in the iron bar.

Nothing remotely interesting has happened in this sequence. Take that horseshoe transformer thing and attach a proper neodymium magnet instead of the iron bar and you'll see quite a bit more power when it's removed.

Or better yet, put the magnet on a rotating thing so that you repeatedly spin it past the horseshoe! Oh wait... That's a normal generator.