Canada

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.