Woah.

For reference, this is Australia’s citizenship pledge:

From this time forward, under God, I pledge my loyalty to Australia and its people, whose democratic beliefs I share, whose rights and liberties I respect, and whose laws I will uphold and obey.

The under God part is optional and most people don’t say that.

No mention of the king.

The key word in “constitutional monarchy” is “constitutional”, not “monarchy”. The monarch must follow the parliament’s requests, and not doing so is unconstitutional. Parliament is sovereign, at least in all of the countries that derive their monarchy from the UK’s.

Outside of the UK there wouldn’t be a fight anyway: in all the Commonwealth countries (except the ones that have since gone fully republican), the monarch has a representative called “the governor general” who is selected by the Parliament and recommended to the monarch at which point see above. The monarch has to take the advice of who is to be their governor-general. Issues basically never get to the monarch for them to mess anything up. The loyal-to-his-country deputy gets first crack at everything the monarch does in theory and has no reason to go against Parliament. If somehow the g-g or the king did speak out, it’d be a legal mess but everyone would ignore them. Practically we’d either get ourselves a new monarch or just say to hell with it and become a republic.

To answer your specific question then, yes, it’s pro forma. The monarch’s role is to be the embodiment of all legislative, judicial, and executive power, in a fairly close analog to what the American Constitution is. But the Constitution can’t exercise any of those powers and the monarch can’t either. It’s just a historical oddity that they can walk and talk, unlike a piece of paper.

In the British monarchy, the monarch (“the Crown”) and the person who is the current monarch are considered distinct “people” with their own separate possessions (i.e. King Charles as the Crown owns property separately to Charles Windsor the private citizen).

So these oaths are meant to be pledging loyalty to the Crown, in its role as the embodiment of the British state, as opposed to the king personally.

The commons library is a treasure trove of information about the UK’s fascinating and complex constitution, I’d strongly recommend giving it a read if you’re interested in this sort of stuff!

Commons Library: the Crown and the constitution

In particular, I’d recommend checking out The United Kingdom constitution – a mapping exercise, which is a document intended to be a reasonably thorough summary of the UK’s constitution and where it comes from. It’s ~300 pages so I wouldn’t recommend reading the whole thing, but it’s great as a reference for the parts you find interesting.

I think “according to the law” is doing a lot of heavy lifting. That is the part that really makes it an oath to the ‘constitution’ of the UK. You are pledging alligence to the figurehead of the government, to obey them/the government, as long as they/the government are acting legally. If the government does something illegal, or asks you to do something illegal, you should not obey them.

I’m British, and not a fan of the monarchy (especially Charles) but I think that we can see the advantages of having a head of state who has very little power to fuck things up, and that isn’t a position that outside forces billionaires can buy their way into, but has the power to remove a Prime Minister if they tried to do something unconstitutional.

The idea of checks and balances in the US didn’t seem to plan for a bad president being elected with enough support in the house and Senate that he becomes pretty much untouchable (especially after a first term stacking the SC).