Australia

I don't think its different as you suggest. Its the individual who has sparked the question, in this case 'ol'under age andy', but they are actually both relationships between government accepted legal instruments.

The Aus-British one is, a Constitution to a Crown and (at least) Parliamentary Legislation of not another Constitution (likely implied i think🤔 The british have a funny informal constitution).

Or the Aus-US, is an alliance pact between countries ratified in their respective countries by congress+POTUS and Parliament+GG

The monarchy is more than a 'set of people'. These people are pampered and wealthy custodians and advisors in the British+Commonwealth context. But the Crown acts as a default of power and ownership that means no one person can ever truly make unilateral claim/title to things. Its a bit of convenient legal fiction that acts very well to represent competing interests and the passing interests of time, unless I've misunderstood how the Crown acts.

Look I don't mind either way he would like it interpreted is fine though. The consequences are of course the important part.

Removing the monarchy from Australia is just as consequential as removing ANZUS, probably larger. This is why I used the comparison. If its going to be suggested that we're going to do it over morality and values of an individual then we'd better apply those principles there-abouts equally in our dealings or they'll soon lose meaning.