Why do you want to know?
I think that the reason this question seems so obscure is because it does not involve sufficient context and specificity. It can't be answered until one knows the reason that it matters to know if a rule is new or not. In a particular context, these questions usually have obvious and clear answers. The murkiness arises only when one tries to overgeneralize.
The life of law is not reason, it is experience. In general, it is almost never fruitful to try to apply legal principles of any kind to their logical conclusion without grounding that logic in fact specific and context specific precedents and applications. That approach to legal reasoning is a classic rookie mistake that gets a lot of young associate attorneys doing legal research into trouble by overstating the confidence that they should have in their conclusions when there is no case right on point addressing a situation.
For example, if a federal government agency publishes something in the federal register that does not exactly restate an existing regulation, then it is a rule change, in the narrow sense that is changes an existing published narrowly defined Code of Federal Regulations rule. The process by which one does so derives from the Administrative Procedures Act and other authorizing legislation passed by Congress and also custom and case law interpreting these, so it isn't self-referential.
A completely different context in which the question of whether there is a "new rule" of law is when a court according to the principles of stare decisis makes a ruling interpreting the constitution in a manner different from or expanding upon previously rulings interpreting the constitution in a similar circumstance. In this context, this matters because a "new rule" of constitutional law is generally given only prospective effect, while an interpretation of an existing rule of law that merely expands upon existing precedents in a foreseeable way has retroactive effect.
In this situation, as in any case in which one tries to determine the best definition to apply under the law, the best approach is to look for a definition that produces just results given the consequences of a particular definition v. another particular definition. In that context, the determination of whether a rule is a "new rule" should depend upon foreseeability and the amount of reliance that people put on the old rule as opposed to the new rule being in force.
There is no good reason to have transsubstantive legal meta-rules that apply to both of these situations. The former mechanistic rule makes sense in its context and makes the status quo clear and the events that constitute a change in the rule clear, while the latter consequence oriented definition makes sense in the completely different context where it is used.
Surely, there are other contexts in which the question of what constitutes a "new rule" could have different consequences still. For example, to determine what constitutes a new v. old rule of U.S. Senate procedure, or to determine which statute is newer or older for purposes of determining which statute of two that conflict should be given effect when there was a cosmetic recodification of the section numbers of one of the titles but not the other without changing the substantive meaning of the recodified statute.
The determination should generally be made on a case by case basis as there is no important purpose served by having a uniform metarule to answer these questions.
If you are getting paradoxes trying to apply your legal theory, you are probably doing it wrong.
For what it is worth, I have a dim opinion of Hart as someone who uses lots of words to say nothing of consequence or use, and I am not familiar with Biagoli or Suber. In general, legal theorists are not terribly influential in how the law is applied and interpreted in practice, although, of course, there are always exceptions.
