I don't know the extent of photos of Harry and Meghan that have been edited before release, but if they have been, there is a difference. The issue with the photo of Catherine and her children is whether it represents the truth in connection with a matter of public concern. There is no matter of public concern for Harry's hair or whatever small vanities produce touch-ups to Meghan's image. In addition, they are private people with no governmental responsibilities. It is different with Catherine. The RF have no real power as such in the UK, but they do have governmental roles and their activities, including matters of their health are legitimate concerns for the public. Yes, of course, Catherine is entitled to a measure of privacy concerning her health, but that measure has limits in a constitutional monarchy. She had no obligation to release anything, but what she did release needed to be accurate.
As to bullying, I'm in the US so I am (thankfully) not aware of what the British tabloids have been up to, but I do know something about the Associated Press, and they are a highly respected news agency with standards that they certainly strive to apply across the board.