You ask
Since the government issues some "proof" (the word used in the Regulations Under the Protection of Word ‘Anzac’ Act 1920) of approval for every commercial Anzac biscuit maker, which need be presented in court if requested, what does this proof contain?
I believe you have misinterpreted the regulation.
According to the linked question, it says
No person shall, without the authority of the Minister, proof whereof shall lie upon the person accused, assume or use the word ‘Anzac’ or any word resembling the word ‘Anzac’ in connexion with any trade, business, calling or profession or in connexion with any entertainment or any lottery or art union or as the name or part of the name of any private residence, boat, vehicle or charitable or other institution, or any building in connexion therewith.
This does not say that the government issues proof to commercial Anzac biscuit makers or to anyone else. It says that anyone who is accused of using the word Anzac in connection with a trade, business, etc., without the authority of the minister bears the burden of proof that they did have the authority.
In other words, "proof" here doesn't refer to a specific piece of evidence but to the act of proving something. In addition to presenting a written document in the possession of the accused, it would also be possible to call witnesses from the ministry to testify, or to seek evidence from the ministry's own records.