Although the Page might, as you suggest, consult with more qualified professionals, the article makes no mention of this. Like Johan, I am not archivist, but I have been a professional historian, of a minor monarchy, for almost forty years and I have worked extensively in the archives of dead rulers and with the archivists in charge of them. Being one HM's valued companions for watching television does not equip the Page to vet HM's papers. Rather the contrary.
As to whether, as discussed above, distinctions should be made between the monarch as Head of State, as head of the Royal Family (can that distinction be meaningfully drawn) and as a private person, the Palace's position, until the fire at Windsor, was that the late Queen did not exist privately.
That is along established position. See:
https://thecritic.co.uk/issues/july-2023/royals-on-the-witness-stand/
That the monarch is still not seen as existing in q private capacity is surely demonstrated by the fact that the late Queen, even when travelling privately, never used a passport. Even Her decision to pay the equivalent of tax following the Windsor fire, was voluntary and did not actually establish her obligation, as a person with PRIVATE resources, to do so.
Consequently, all of her papers should be considered, if not public, at least susceptible to archiving.
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