I’m pretty sure that (for instance) Australia was just hanging on until we could be sure she was gone, the current government have already planned a referendum on it in a few years if they get a second term.
(I say ‘we’, I am a relatively recent British migrant, and not a citizen yet)
1. There was a sense of loyalty to Liz personally. She did a good job of Queening and it seemed almost rude to interrupt that.
2. No-one wants Charles as king. He's very weird, and has ideas that he actually wants to do things with.
I fully expect the referendum to be brought forward because of her death, and for it to get a strong "yes".