No, the Commonwealth Realms are in, at most, a personal union with Britain. I’ll use my native Canada as an example. The Queen of England just so happens to be the Queen of Australia, as she just so happens to be the queen of a group called the Commonwealth Realms. The Queen has the power to require all legislation to have Royal assent and she can appoint a Governor General to do so on her behalf. This power, though, is shared with parliament, and largely ceremonial anyways. Canada, and for that matter all the other Commonwealth Realms, are completely independent from the UK (well the UK isn’t really independent from the UK because the UK is the UK but you get the idea). When they weren’t independent, many of the Commonwealth Realms were directly ruled by the United Kingdom, and there was very little native governance whatsoever. The exception to this are the British Dominions, which were able to operate effectively as independent nations, yet remained part of the British Empire. Even the Dominions, however, could be subject to the British Parliament altering/creating legislation in their Dominion without approval from the colonial government, which is a power that British Parliament doesn’t possess now, and hasn’t possessed since 1982, 1986, and 1986 for the Dominions of Canada, Australia, and New Zealand respectively. To summarize with a simple analogy, the Queen of England (as a title) doesn’t have power in Canada, yet the Queen of Canada does. These two roles, however, are occupied by the same person.
