Example of one I didn’t know:
Australia and Canada did not become fully independent until the 1980s.
“The British courts still heard final appeals from the courts of the dominions. In 1982 for Canada, and 1986 for Australia, Britain finally renounced its control.”

Technically this is true. Until 1982, Canada technically remained a creation of the British Parliament. While Canada effectively functioned independently, via both law and custom, those laws and customs were under the theoretical control of Britain to vary at any time, including by potentially revoking Canada’s functional independence. It was only with the ‘patriation’ of the Canadian constitution to Canada in 1982, with the agreement of Britain, that Britain lost all control and Canada became fully independent.
At a functional level, however, Canada had gradually become more and more independent from the time of its confederation in 1867. It effectively became entirely self-governing in 1931 (subject to the theoretical ability of Britain to revoke this, as described above) through the passage of the Statute of Westminster in 1931. That said, appeals from Canadian courts in certain cases were still heard in Britain until 1949, though after 1931 that was at the choice of the Government of Canada.
I believe it’s also true to say that part of the reason for the late repatriation of the Canadian constitution was opposition from some First Nation tribes which had made treaties with the British Crown which they weren’t convinced would be upheld by a Canadian government.
In any case, King Charles III remains Head of State of a surprising number of countries, but not because they are part of the ‘British Empire’, simply because he is also King of Belize, Australia, Jamaica, Canada etc.
This is not a bad thing: unlike POTUS, the British Monarch has no executive power at all. He can’t give orders to the Armed Forces, appoint judges or order the assassination of supposed enemies, except when told to do so by the democratically elected government of the countries where he is Head of State, thus separating the Government of the Day, from the State itself. A neat solution.
The observation about Indigenous rights is a fair comment. But I would add that, even more fundamentally, the delay for Canada in patriating its Constitution was due to a lack of an ability between the federal government and the provinces to agree about a new constitutional document. There was also a degree of inertia, with some seeing little need to go ahead with the process of getting a fully patriated Constitution given that the Canada was already governing itself independently at a functional level.