Why Prince Harry and Meghan Markle's children are now Prince Archie and Princess Lilibet

ok.co.uk:

In the aftermath of the Queen’s death, many members of the royal family have seen change in their titles as King Charles takes to the throne.This also includes Prince Harry and Meghan Markle’s two children Archie and Lilibet who will now be able to use HRH titles, according to royal protocol.The changes come after the children’s grandfather became King Charles III and should they so wish, three year old Archie can be called a prince and his sister Lilibet, one, princess.

Rules set out by King George V in 1917 mean that Archie and Lilibet, as the children of a son of a sovereign, may use an HRH title if they wish.

The rule is the reason why Prince William and Kate Middleton’s title were referred to as prince or princess, while Harry’s were not - until now.This rule was established by King George V after he issued a Letters Patent in 1917 that read: "…the grandchildren of the sons of any such sovereign in the direct male line (save only the eldest living son of the eldest son of the Prince of Wales) shall have and enjoy in all occasions the style and title enjoyed by the children of dukes of these our realms." Speaking about these changes to People Magazine, Joe Little, managing editor of Majesty magazine said: “As the grandchildren of the Sovereign, they have the right to be upgraded to the style of His or Her Royal Highness.

But that begs the question of whether Harry and Meghan want that.” He added: “Do they prefer what [Prince] Edward and Sophie have, and not have their children as Their Royal Highnesses with a view to them leading relatively normal lives?" This appeared to be the case previously with the Duke and Duchess of Sussex rejecting the "courtesy title" of Earl of Dumbarton upon Archie’s birth, instead.