Turning into superconductivity---continuous or discontinuous?

The figure below is Onnes' original data.

The transition region is very narrow. It suggests a first order phase transition, but still not so conclusive.

What is the latest understanding of the transition behavior? Is it continuous or discontinuous? What is the scale behavior?

For a superconducting transition, the order parameter is roughly the superconducting gap (it is a bit more complicated than that, but for this discussion the gap is enough). The gap is finite in the superconducting state and zero in the normal state. It does vanish continuously and behaves as $$1 - (T/T_c)⁴$$ close to $$T_c$$.