Maybe I'm misunderstanding but since this 3D CPU would be superconducting, it would conduct electricity without resistance and therefore not generate any heat while in use.

If you went a bit colder you could use superfluid helium and laser cut microchannels through the whole die. You would need to cool it to 2K and every degree at that temp is a fight but once past the transition point it becomes a remarkable thermal conductor and loses all viscosity. It seeps through tiny pores in porcelain like it's a sponge.

Presumably 80x less power including cooling means more than 80x less power not including cooling.

I'd think that should be enough to get quite a few layers, sure maybe some minimal space between layers for cooling, but radically less than the non-superconducting designs.

Could a design with gaps between layers, but still connected as one not mitigate that though?.