An upcoming US Supreme Court case may impede AI governance efforts

I don't think I see the problem. Chevron deference is, as you say, about whether courts defer to agencies interpretations statutes. It comes up when an agency thinks one interpreation is best, and a court thinks a different interpretation is the best reading of the statute, but that the agencies prefered interpreation is still a plausible reading of the statute. In that case, under Chevron, the court defers to the agencies interpreation. Do away with Chevron, and the court will follow what it thinks is the best reading of the statute. This is, I should note, the background of what courts usually do and did before Chevron. Chevron is an anomaly. 

In terms of implications, I think it is true that agencies will tend to interpret their mandates broadly, and so doing away with Chevron deference will, at the margin, reduce the scope of some agencies powers. But I don't see how it could lead to the end of the administrative state as we know it. Agencies will still have jobs to do that are authorized statute, and courts will still let agencies do those jobs. 

So what does AI regulation look like? If it looks like congress passing a new statute to either create a new agency or authorize an existing agency to regulate AI, then whether Chevron gets overturned seems irrelevant - congress is quite capable of writing a statute that authorizes someone to regulate AI, with or without Chevron. If it looks like an existing agency reading an existing statute correctly to authorize it to regulate some aspect of AI, then again, that should work fine with or without Chevron. If, on the other hand, it looks like an existing agency over-reading an existing statute to claim authority it does not have to regulate AI, then (1) that seems horribly undemocratic, though if the fate of humanity is on the line then I guess that's ok, and (2) maybe the agency does it anyway, and it takes years to get fought out in court, and that buys us the time we need. But if the court ruling causes the agency to not try to regulate AI, or if the years long court fight doesn't buy enough time, we might actually have a problem here. I think this argument needs more details fleshed out. What particular agency do we think might over-read what particular statute to regulate AI? If we aren't already targeting a particular agency with arguments about a particular statute, and have a reasonable chance of getting them to regulate for AI safety rather than AI ethics, then worrying about the courts seems pointless.

I am a law student between my first and second years.

I would estimate the probability of an overruling of Chevron in Loper Bright Enterprises v. Raimondo to be at least 85%. Gorsuch, Thomas, and Alito are >99% votes in favor of such an outcome. Among Roberts, Kavanaugh, and Barrett, I think it very likely that at least two join. If this kind of thing interests you, I recommend reading Gorsuch's concurrence in Gutierrez-Brizuela, a 10th Circuit case (<https://casetext.com/case/gutierrez-brizuela-v-lynch> scroll down to find the concurrence), as it is probably representative of the kind of reasoning that an overruling of Chevron will involve.

While overturning Chevron deference seems likely to have positive effects for many industries which I think are largely overregulated, it seems like it could be quite bad for AI governance. Assuming that the regulation of AI systems is conducted by members of a federal agency (either a pre-existing one or a new one designed for AI as several politicians have suggested), I expect that the bureaucrats and experts who staff the agency will need a fair amount of autonomy to do their job effectively. This is because the questions relevant AI regulation (i. e. which evals systems are required to pass) are more technically complicated than in most other regulatory domains, which are already too complicated for politicians to have a good understanding of.

Why do you think that the same federal bureaucrats who incompetently overregulate other industries will do a better job regulating AI?