Afaik, your intuition is basically right! A superconductor exhibiting only the Meissner effect won't hover ("pin").

It's a defect (where small amounts of the field aren't expelled) that allows for the pinning to happen: https://en.wikipedia.org/wiki/Type-II_superconductor#Flux_pi...

I think that for true hovering demos the trick is to cool the super conductor to below its critical point while it’s already inside the magnetic field. Then any way you move it will immediately induce a reacting current in the superconductor that will move it back into place. Exactly the same place since it’s a super conductor and has 0 resistance. I think in these demos though it is the fact that one side is heavier and dragging that’s leading it to stay in place

My laymen’s interpretation is that superconductors perfectly expel the magnetic field without distorting the field and so can sit in a position that is effectively locked and held in position. I could be completely wrong however.

There's a noticeable distortion of the magnetic field near the superconductor. It's this distortion that keeps the superconductor stable - it's caused currents that appear on the surface which match and cancel* the surrounding field.

*some of the magnetic field penetrates onto the surface of the superconductor, but internally, there's 0 magnetic field within the superconductor.

When a superconductor interacts with a magnetic field, currents generate at the surface of the superconductor that will produce their own magnetic field, which cancels the external one. The superconductor doesn't fall out to the sides because the field gets cancelled and there's no net force acting on the conductor.

There can still be torque (i.e. rotations) for type I superconductors, and type II superconductors when they're fully superconducting. I'm not familiar with how the specific dynamics work though - I'm guessing it's related to gravity?