Yes, it's already partially codified in many places, and the courts use their internal procedures even where not.

Still, in the USA for example, the Supreme Court has ruled that contempt is a privilege of the courts. It is not subject to such things as the right to trial by jury. A person can, in actual practice, end up in prison for decades without ever having been charged with a crime or having gone before a jury: https://www.nytimes.com/2009/07/12/us/12contempt.html

I'm more familiar with it here in Canada, though it's my understanding the basic concept is the same in many US states still. It is the last vestige of true common law. Which is really quite an unusual situation. Authority is derived directly from the head of state through the judicial branch. While laws that the legislature has passed, like the constitution, do restrict the courts, they pretty much otherwise make it up as they go. In the sense of how the old common law system always worked.

When the logging companies vs. environmental activist issue in British Columbia was very hot a couple decades ago, a whole stream of injunctions got issued and some case law had to be spun up real quick on people willfully and publicly defying injunctions. It was odd to read judges debating whether they should criminally sentence people for contempt in accordance to the Criminal Code's general sentencing provisions or not. After all, they don't have to, as statute doesn't require them to. In one case on appeal, the BC Supreme Court decided it would be very prudent to adopt that as the standard used, and so that's now precedent at least.

I guess the question here is whether there is any need for a meta-meta-judicial system, given that court orders by and large already have a path of appeal, and that most orders that lead to contempt charges cause no irreparable harm.

This case is a perfect example. All he has to do to be freed of house arrest is turn over his devices. He has this objection about attorney client privilege, which he may prevail on (though it doesn't seem likely). But he or his client could always seek later judicial remedy in the unlikely event that that privilege is violated as a result of Chevron's searching for evidence related to this case.

It's also worth noting the protracted nature of his confinement is partly due to a lot of legal wrangling that's been going on, not all of it on the side of the court. For example, the trial was scheduled to occur in September last year, but Donziger's lawyer asked that it be postponed because they didn't want to have it virtually.