It's mostly (>60%) a mix of solar and wind power, with some gas that fills in the gaps - as well as batteries for grid stability. Still importing some coal power from interstate, but that is decreasing too.
The investment has been incremental - so much smaller amounts, with much less risk and therefor more attractive to investors.
A large part of this (since 2018) has been done by a conservative state government, who have been highly supportive of the renewable transition.
https://theconversation.com/against-the-odds-south-australia...
To answer more directly though, yeah the power is the same cost. Perhaps when renewable penetration into the energy market is saturated, there will be a greater demand for base load at all those times renewables aren't producing at peak, and that will be reflected in those nuclear MWHs becoming very profitable even at a higher unit cost.
you gotta compare like-for-like. If the solar project that takes 2 years only provide power half the time, then you need double the size to provide the same amortized level of power at night. You also need some form of storage. And that's if you don't have a spate of bad weather preventing it from working - so to amortize that problem you'd need to build yet larger...