ETA: the video referenced is apparently available at https://www.youtube.com/watch?v=EtVjGWpbE7k . Interestingly, posted on Feb 26, 2023.
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.
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.