To clarify: "The Crown" is often a short-handed statement for the executive government, which is basically the Cabinet for the PMO (Prime Minister's Office) - all the Ministers of different government departments. Symbolically, they work in the interest of the de jure (written in law) authority of Canada, which would be the Monarchy in Britain (who is also symbolically head of state for every other Commonwealth nation). Now, as to touch on the British Commonwealth (since "The Crown" in Canada would basically be decimated in a conventional confrontation with the US):
It would turn into an existential crisis for everyone, I assume. A lot of "every man for himself" sort of mentality, but I assume there would be those who would want to fund a Canadian resistance (even if paltry) simply on the notion that an Imperial America is a FAR worse threat than anything Europe had faced before (expansionist policies, current global economic power, utterly disconnected from mainland Europe and the largest navy and airforce combined... kind of a worse situation than Fascist Germany, since it would be far more difficult to deal any direct damage to US infrastructure from the other side of the pond).
I'll be honest, I would have no idea if the Commonwealth would actually step up in a way that is remotely similar to what we have done for Ukraine. I would honestly expect more help from Mexico and Latin Americans than I would the Commonwealth, as they would see that the US would be a very tangible threat at this point and also share the all-too-important land boarder.
Simple why it's so effective:
Institutions are facing increasingly insurmountable problems, and people are not dealing with the consequences and stress that comes from these problems. They want answers and solutions.
Institutions ask for you to have patience and give them time to fix the issues. Problem: people already don't believe that the institutions are fixing things, so you can't rely on them to fix it. The solution, they feel, has to come from elsewhere.
Left-wing propaganda says that the institution is broken, they will fix it. They want to take the money away from the ultra rich and give it back to the public as a form of equalization. If you are part of the ultra rich, you don't like this.
Right-wing propaganda says the institution is broken, they will fix it. Right-wingers generally believe in the accumulation of capital for themselves via "merit", which means the upper class and billionaires are likely to be supporting / using them.
People believe that things need to be fixed (which is likely true). Only left-wing and right-wing propaganda say that the institution needs to be fixed, it definitely isn't coming from the institution itself.
The ultra rich fund whichever propaganda will allow them to retain their own benefits and works to suppress the propaganda of the ones who work against their interests.
Hence, right-wing propaganda is massively inflated to support fixing a system that allows retaining wealth, while they suppress left-wing propaganda which says wealth needs to be redistributed to the masses.