What would happen if you forced the magnet to move faster over the inclined copper bar? Would you feel resistance from the magnet? The answer might provide more information toward the solution to the phenomena?
My explanation for all of this is: aaaaAAaaaAAuAAAaaa 😂. I've watched videos before on this effect but you showed us a lot more examples which was really cool.
I have found the thickness is important. I Have only really tested the different thicknesses on aluminum, but there is a very apparent different in thin vs thick aluminum. It is tough to find the really big copper or aluminum. I've been wanting to try this experiment for years, but a big piece of copper or aluminum was always the hold up for me.
I'm not done with the video, so maybe the answer is provided. But you're seeing electrical resistance, which manifests as heat. This is literally what an incandescent light-bulb is -- it's a controlled "short". The heat is probably too minimal for you to detect it via touch, particularly when the enormous copper bar is a fantastic heat-sink all by itself. You could potentially test this if you attach the magnet to a wheel and have it pass closely over the copper plate repeatedly for a long period of time. Then the heat build-up should be detectable to the touch.
It is sort of unreal. I really would love to understand it a little better so I got a handful more experiments to do. Electricity and magnetism is really fascinating and weird!