SCOTUS is 100% the gatekeeper of state laws when they violate civil rights. They are also the gatekeeper of errors of law at lower courts. That is in fact their job. But that does not mean they decide how the courts work in terms of process, and it does not mean that being denied a a TRO or injunction is a misapplication of the judicial process.
This particular suit has a lot of issues. At least from the bits I've read, and temper my opinion with the fact that I haven't been watching the wrangling on this one, so I may be missing a lot of stuff.
So first up is the question of standing. Standing, unfortunately, requires harm. In the case of civil rights stuff, the fact the law is clearly harmful often isn't sufficient, you have to actually step up and be harmed in most cases. TROs and injunctions do tend to deal more with unavoidable harm, but you still have to demonstrate that you will be harmed, not that you might be.
So first up, like half the arguments are that you can't regulate us like this because 2A. I doubt the court is going to see that the state does not have great leeway in regulating the operation of a business. If regulations are going to get canned over the 2nd, it's going be because they infringe the rights of an individual in the end.
An example of a shit claim in the case: NYS can't require a POC implementation of NICS. NICS is a federal law and very clearly allows for a POC implementation. That would be a totally different suit and I'm not sure why it is even here.
A more ambiguous claim in the case: They are creating a registry and the 2A and 4A says you can't. Well, is there actual case law on this. There are opinions, and legislation around said opinions, but not case law. It's a valid challenge, but do the FFLs have standing? Have they been harmed? More importantly is that harm irreparable? A registry can be destroyed, and if actually destroyed, the harm it does is gone. You are not likely to win a case with the argument that the people running the registry are scumbags and can't be trusted to work that way.
A different ambiguous claim: That the laws will put them out of business due to cost. While one can argue that unlike the other amendments, the 2nd really does kind of require commerce, so things that effectively forbid a commerce in arms can be infringing. The suit claims that compliance will cost $200,000-$1,000,000 to comply with, and I have yet to see where they get that number. From what I've read, it sounds unlikely to be accurate. So they may have standing potentially, but have they demonstrated inevitable harm? A lot of things on the list likely ARE 2a violations, but the winnable case is going to come from the customer side of things, not the business side of things.
It does not strike me as a particularly strong case in general, and specifically I don't think what merits it does have lend themselves particularly well to winning TROs or injunctions.
I mean really, are security systems expensive to the degree that it is an existential threat to anyone being able to operate a business? Is there something special about that requirement with regards to this law that makes it move from something private households and small bodegas can afford, but not FFLs?