> I am not even sure whether logical components work at such low temperatures, since everything becomes superconducting.

Currently finishing a course where the final project is designing a semiconductor (quantum dot) based quantum computer. Obviously not mature tech yet, but we've been stressed during the course that you can build most of the control and readout circuits to work at cryogenic temps (2-4K) using slvtfets. The theoretical limit for this quantum computing platform is, I believe, on the order of a million qubits in a single cryostat.