By law, what are the duties of the Queen that only she can perform and which can she pass off to Charles without abdicating? I’m not counting actions that only require her signature. I can only think of opening Parliament. I know she meets with the Prime Minister weekly, but is that required?
I have no actual citable facts, but I think that she could take to her bed and let the rest of the ‘Firm’ get on with it.
She doesn’t have to open Parliament in person and indeed the present Queen hasn’t done so on a couple of occasions (when she was pregnant). She just appoints several commissioners to stand in for her, which is what she invariably does for its closing ceremony. Nor does she have to meet regularly with the Prime Minister, although it could be argued that the Prime Minister has a right of access to her and so could insist on a meeting.
Actually, signing things is the one duty that not performing would cause problems. However much a formality, she usually signs documents because their importance is such that they require her personal authorisation. But there have been cases of monarchs in old age, such as Henry VIII or James I, who have delegated even that by allowing officials to use a stamp of their signature.
The only one of her duties that she could not at all delegate was giving birth to Charles . . . plus a few backups.
The only thing which is not delegatable is any constitutional changes to the statuses of the Church of Scotland and the Church of England as state churches.
Her Majesty has two duties under the Constitution of Canada that cannot be performed by the GovGen: the appointment/dismissal of the GovGen, and directing the GovGen to appoint additional Senators under s. 26 of the Constitution Act, 1867. As far as I know, no steps have been taken under Canadian law to allow her to delegate those tasks.