I do agree that this was handled badly by Charles. Either make it clear at the start that his grandchildren by his youngest son, unlike the children by his mother's youngest son, will be known as prince/princess or announce that going forward the titles are only reserved for the children of the monarch and future heirs, continuing the precedent set for the children of Edward and Sophie. This 'in-between' and unnecessary wait was ill-advised (or decided ?).
Charles could not actually change anything until he ascended. QEII could have changed the titles and chose not to.
My read between the lines is that Charles did make it known to Harry and Meghan, and I suspect Edward and Sophie, that his wish would be for the monarch's grandchildren by the non-heirs apparent not be given titles. If my suspicion is correct, Edward and Sophie complied with Charles' wishes and when their children were born they were not HRH Prince/ss, whereas Harry and Meghan wanted their children to have titles and were not willing to comply with Charles' wishes.
The whole skin tone brouhaha from the Oprah interview was tied to titles. Firstly Harry and Meghan wanted their children to have titles from birth because according to them the child would get security if they were bestowed the HRH Prince/ss title at birth. Secondly there was the discussion that Harry's children would not be HRH Prince/ss when Charles ascends which according the the LP issued by George V, they become HRH Prince/ss when their grandfather ascends, but it was made known that going forward only the heir apparent's children are HRH Prince/ss. Meghan made it clear that she thought this was unfair because the future KC3 would have one set of grandchildren who were HRH Prince/ss and one set that were not, and in Meghan's eyes, that was unfair, and furthermore also not a good move because the first BRF child of color would not be titled. According to Meghan, "it’s not their right to take it away".
So basically the Sussexes made it known before their child was born that their wish was for their children to have titles from birth, and if not that, that the George V LP be adhered to.
For Charles to get what he wanted, he would have to issue his own LP and either make it going forward, or if he wanted it to apply to existing HRH Prince/ss, he would have to designate which ones, all of them which means that the Duke of Kent would lose his HRH Prince title, or certain ones, and if not all of them, then what was the cut off point and why.
Of course what he could have done was upon his ascension, when the website was updated to to change his, Camilla, William, Kate and their children's titles, also update the titles of his Sussex grandchildren, especially since he probably realized that he was not going to make any changes that would result in retroactive removal of titles.
I get why Charles did not update the website, my understanding is that he wanted it to be clear that the Sussex children have the HRH Prince/ss titles because their parents wanted them to have the title, so he let them be the first ones to refer to their children as HRH Prince/ss which they did when they released a statement about Lili's christening.
To me, it was not handled badly at all, if anything, I think that it was a smart move on Charles' part to let the Sussexes out themselves as being hung up on titles, although it was not as if that was not already very apparent to more than a few royal watchers.