Prince George, Princess Charlotte and Prince Louis were all registered as 'HRH Name of Cambridge' on their birth certificates.
As pp's have said, their given names became 'HRH Name of Wales' when Prince William became PoW.
The York girls were born HRH's, so were also styled as 'HRH Name of York'.
Lady Louise and Viscount David (when born), children of Prince Edward and Sophie were not born HRH's. Their birth certificates have their surname as Mountbatten-Windsor, although they used just Windsor at school (not Wessex).
Both Archie and Lilibet's birth certificates show their surname as Mountbatten-Windsor. Lili's looks very different in style as obviously it's a US birth certificate.
I think (although fully prepared to accept my understanding is wrong) the difference is that Harry & Meghan have chosen Sussex as a surname for Prince Archie & Princess Lili when neither of the children are HRH's.
I suppose the situation is unprecedented in that Harry & Meghan are still HRH's, but agreed not to use this title. Even if they started using HRH again, the children are not HRH's so wouldn't use Sussex as a surname in the UK.