The fossil fuel industry is not funding pro-nuclear arguments because they want to see 50% of their business lost to nuclear. They are not worried about losing huge profits to nuclear because from a purely economic perspective nuclear is not cost-competitive with fossil fuels. Hence it doesn’t pose a major threat, absent massive government-subsidized build-outs (which aren’t remotely on the table now.)

The fossil fuel industry is funding pro-nuclear PR because they realize that renewables do pose a major economic threat to their business in the short term, since they are now cost-effective enough to replace vast chunks of their business (even if not 100% of it.) Pro-nuclear (and coincidentally anti-renewable) PR is the most efficient way to protect their business. If they can convince the public [incorrectly] that the best way to decarbonize rapidly is to abandon/block renewable build-outs because “nuclear is the only way” then they’ve paid enormous dividends to their shareholders.

If your response to the above is “these random technical points are correct, what’s the problem”, then the problem is: those random technical points are largely a distraction from the important questions of how we decarbonize quickly. The fossil fuel industry understands this perfectly, because they have a lot of skin in the game.