I’m still not sure what you mean by this. Maybe you need to explain better what you want?
Here’s a test with a real magnet and a ball bearing:
I think this proves that magnets do cause objects to orbit (kinda). That nudge in the trajectory basically is just that: an orbit. Just not a stable orbit, and the object will quickly either escape, or fall into the magnet. If I remove gravity (pencil) from my experiment, the magnet wins and this causes a very eccentric but small orbit around the magnet. It looks more like vibrating than orbiting. My code behaves just like this realworld experiment.
In your videos you have a pretty realistic behaviour. I think it would be a fun mechanic if you just balance the forces to make it feel good. But I understand that in games the desired behaviour is not always the most realistic one.