Pricing carbon would mostly drive fossil fuels from the grid (unsurprisingly). It might boost nuclear as a result but it would boost renewables far more.
Ultimately it's about energy return on investment.
Solar + battery requires plenty of materials and energy to put together. It also needs to work in the middle of winter for it to be a fair comparison. When you consider it in that way it favours nuclear. It also has a shorter lifespan than nuclear, so that should be included.
Energy return on investment is pure crankery. It's a meaningless number that has basically no impact on any decision.
And, if you take that crankery seriously, then renewables vastly outperform fossils and are speeding past nuclear on this metric too.
It's basically impossible for energy tech to come down in price by magnitudes and not have increasing EROI as energy inputs cost money. This is predicted to continue.
And despite this metric being great for renewables, you don't hear anyone crowing about it, because it's meaningless.
Even decade old solar was competitive with nuclear on a carbon per watt basis:
https://ourworldindata.org/safest-sources-of-energy
Pricing carbon would mostly drive fossil fuels from the grid (unsurprisingly). It might boost nuclear as a result but it would boost renewables far more.