> audit itself is illegal or unconstitutional
The audit might be unconstitutional because it's coming from a department which is wielding a great deal of Article II power even though it's not led by a cabinet official who was confirmed by congress. In other words, unconstitutional for organizational reasons that are unlikely to land any one person in criminal trouble. I wouldn't want to argue that point either way, but I bet the question of DOGE's constitutionality will be considered by a federal court in the coming years.
The notion that the audit is illegal because of "technicalities" is a lot more sympathetic. The handling of secure information in the government in unorthodox ways can be deemed to violate the law, or not, in some surprising (or maybe even arbitrary) ways. The last really big time this played out politically in the US was probably Clinton's email server.
As I hinted at above, I don't think anyone here is really conversant with that area of the law. On the other hand, I'm fairly certain even if DOGE has broken the law, the current DoJ will not find that DOGE has done anything requiring legal action, for the obvious political reasons.