No - it means that Charles III is an independent monarch for two separate nations.

The monarchy is 99% ceremonial in Canada but it's important to note that the Canadian Crown isn't the UK Crown... Canada is not a dependent of the UK in anyway, simply the person that wears the Crowns is the same person.

https://en.wikipedia.org/wiki/Monarchy_of_Canada

>the Crown has had both a shared and a separate character: the sovereign's role as monarch of Canada has been distinct from their position as monarch of any other realm,[n 4][16][65][66][67] including the United Kingdom.[n 6][69][70][71][72] Only Canadian federal ministers of the Crown may advise the sovereign on any and all matters of the Canadian state,[n 7][70][73][74][75][76][77] of which the sovereign, when not in Canada, is kept abreast by weekly communications with the federal viceroy.[78] The monarchy thus ceased to be an exclusively British institution and, in Canada, became a Canadian,[40][79][80][81] or "domesticated",[82] establishment, though it is still often denoted as "British" in both legal and common language,[40] for reasons historical, political, and of convenience.

Let me introduce you to the Commonwealth of Nations

https://en.wikipedia.org/wiki/Commonwealth_of_Nations

These countries choose voluntarily to hold ties with the UK, and each other, and some accept the UK's monarch as nominal head of state, but don't be mistaken; they are all fully independent countries. Some are republics, some are kingdoms with their own monarch. They value each other's friendship, shared values and heritage, but they're not beholden to the UK or each other.

No, it’s like Elon. He happens to be CEO of multiple companies but they are separate and independent companies (for now).

No. We have our own monarch who happens to be the same human is all

No. He is separately the monarch of the UK and Canada. You could just as well argue that the UK is dependent on Canada for that reason.

No, he’s just the monarch of two different countries simultaneously.