Although Prince Harry reached out to King Charles III amid His Majesty’s cancer struggle, Kate, Princess of Wales, has no interest in seeing or talking to her brother-in-law during her own health battle. “I think there was once a relationship, a friendship, a very close one between Harry and Kate,” royal scribe Christopher Andersen dished. “I’m sure he’s concerned about her as well, but I know that she wants to have nothing to do with them.” Her Royal Highness “still feels betrayed” by the fifth in line to the throne, just as the King, and “especially” her husband, Prince William, do. Andersen…