Before I looked at the details, I thought it was electromagnetically driven. Combine that with a power outage, and you’re hunting for little steel balls on the floor. But at least you’d know when the power went out, based on which ones are missing from the base.

I wonder, is it possible to make a magnet that's always on and uses power to switch it off? Kind of like how air brakes on trains work.

There are classes of relays that worked like that in old portable broadcast video recorders. Essentially a coil around a magnet and the coil was used to strengthen or weaken the flux with a pulse of current. The armature was spring loaded but not strong enough to release from the permanent magnet unless a pulse of "buck" current was applied.

Old timey stuff.

Yes, you add a magnet in the middle of the coil and actuate the coil with opposite polarity to cancel the magnetic field

Maybe, but I probably wouldn't try to use them for that. Instead I'd look into getting some kind of latching solenoid to move the real magnets in and out of position. That'd let you have it be silent (or nearly so) and not need to keep the magnets energized the entire time, reducing power usage. Then steppers for the rotation and platform lift