The NRC (and most other regulatory bodies) predate Chevron deference, so you should count on them sticking around and still doing their thing. A nuclear startup could try taking them to court to circumvent all their rules and build naked nuclear piles in residential neighborhoods or something, but even if they got a federal judge to go along with that, it should be an easy political win for legislators to smack it down with some new more specific laws.

And although the regulatory interpretation of those laws could also be challenged in court, successfully doing so shouldn't be considered a given. Judges generally do have some sense you know, as a class they decide important matters in boring uncontroversial ways across the country every days. The controversial outcomes that make news cycles are newsworthy specifically because they're unusual.