The King in his capacity as Head of the Commonwealth does not have to follow the advice of any government minister of any realm. I think therefore he should put out some sort of statement regarding the territorial integrity & sovereignty of all his Commonwealth Realms whilst at the same time in his capacity as King of the UK welcoming POTUS.
And what an utter embarrasment Starmer was when asked the following question :
"did you discuss, with President Trump, his repeated statements of desire to annex Canada, and has the King expressed any concern over the president’s apparent desire to remove one of his realms from his control?”
Indeed, Starmer refused to answer that question. In fact, he said in response thereto, that "there was no divide between the US and the UK", or something like that.
Still, the (American?) reporter who asked the question framed it incorrectly asking how the King felt about Trump trying to take away one of the King's realms "from the King's
control". Starmer could have taken the opportunity to clarify to the reporter what the role of the King in the realms is. However, the question was clearly a provocation aimed at driving a wedge between the British government or the Royal Family and Trump, and Starmer was correct in my opinion not to take the bait.
The King does not have personal responsibility for foreign policy or external relations in Canada or any of the realms. "Head of the Commonwealth" on the other hand is a honorific title that has no constitutional meaning in Canada either. Buckingham Palace, despite many provocations, has consistently refrained from making any comments on the Trump/Canada affair, and it is absolutely right that the King should make no comment. The official position of the King of Canada (as a legal entity rather than an individual person) on this issue has to be conveyed by the King's responsible ministers in Canada.
EDIT: I am sure that some observers in continental Europe will come out tomorrow criticizing Starmer for "cozying up" to Trump while the PM tries at the same time to claim a united front with Europe, which, for some Europeans, brings up the usual "perfidous Albion" vibes. However, as I see it, that is just the Brits doing what they excel at, i.e. quiet diplomacy, keeping calm and carrying on. Quite frankly, some of the inflammatory remarks and emotional responses from European leaders with respect to the USA in recent days have been counter-productive and ineffective, especially in Germany. The Brits and, to be fair, President Macron seem to be approaching their relation with Trump in a more pragmatic and efficient manner.