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.