The King's spokesman explained the lack of update a few days ago:
https://www.dailymail.co.uk/news/ar...ted-Master-Miss-updated-succession-order.htmlThe King's spokesman said the monarch had announced William and Kate's titles as the Prince and Princess of Wales, and expressed his love for Harry and Meghan in his address to the nation on Friday.
'While the website was updated for the Waleses, clearly updating love on a website doesn't quite work so we've not quite done that but clearly he does love them. We will be working through updating the website as and when we get information,' he said on Saturday.
https://www.thesun.co.uk/news/19768951/meghan-markle-prince-harrys-children-titles/Asked whether Archie and Lilibet would take the titles of prince and princess, [the King's spokesman] said: "At the moment, we're focused on the next ten days and as and when we get information, we will update that website."
More recently, he stated (apparently in answer to the "tense discussions" report) that title discussions and announcements are unlikely to occur before the end of the mourning period on September 26:
https://www.dailymail.co.uk/news/ar...ie-Lilibet-not-announced-period-mourning.html
And yesterday [September 14] a spokesman for King Charles said it was ‘unlikely’ that any announcement would be made until at least September 26, when the period of royal mourning ends.
They told the Daily Mail: ‘The King is focused on the mourning period so it is unlikely [any announcement would be made] on other titles during that period.
‘The future is an amazing thing. I am sure that at some point there will be discussion, but not during the royal mourning period.’