Yeah, that thing does really want to stay in a constant level on the magnetic field. That would dispel every other explanation on the GP, as it's not simply being repelled or attracted.

I found that video very compelling. If it was eddy current, the float standoff distance would have decayed. It sure looked to me like there was no decay at all, and wow! if true.

What is float standoff distance?

Eddy currents can be induced in non-superconducting materials that make it look like levitation, but the catch is that there has to be relative motion between the magnet and the object 'levitating' to generate the currents in the first place.

I've linked to a relevant example in a Veritasium video here: https://youtu.be/g0amdIcZt5I?t=543

But in this sample video, the standoff distance doesn't appear to be slowly dropping at all, which would rule out eddy currents as a source of the behavior. If you continue watching the linked video to 13:27, he talks about how and why superconductors levitate.

Electromagnetic solenoid designer here...

Copper and a magnet can certainly interact. Drop a magnet through a copper pipe and the eddy currents will induce a field that's opposed to the magnet causing a damping effect. Maybe something like this is going on where movement of the magnetic field is inducing an opposed magnetic field in the copper, and thus interacting.

Anyhow it will be interesting. if It can generate a field of 1.5-2 Tesla you could have more efficient solenoids and probably motors.