many have also pointed out that the British press seems to have left Kate alone and not pressed for more info, while Meghan was essentially left out to dry by the institution and was subject to abuse by the media while pregnant with archie and suffered a miscarriage in 2020
Firstly, I don’t think it’s entirely true that the British Press “seems to have left Kate alone and not pressed for more info”. The British and global press have in fact been writing continuously about Kate’s absence since the news of her operation was released in mid January. There were immediately press teams from around the world set up outside the hospital. They will have been digging around too I am sure to find out if there was any information they could find out about what her health condition is.
What the press haven’t done in the UK is publish anything about what they may or may not have found. The main reasons for this is that they aren’t allowed to. Under the Human Rights Act 1998 everyone (yes, even the Royals) has the right to respect for their private and family life. The state of your health falls very much under your private life.
This was very much the case for Meghan as well. Archie was born in May 2019. The press were not publishing abusive stories about her state of health while she was pregnant. They speculated about nursery paint and decoration, names, godparents - all fairly normal press pieces for a famous woman going through a pregnancy. In fact at that time her coverage was mostly positive - remember Harry said of their trip to Australia and New Zealand while she was pregnant that he thought the family was jealous because her coverage was too positive? The only really negative story I can think of was her trip to New York by private jet for a lavish baby shower, which was criticised - but’s that’s legitimate of her publicised actions (the baby shower was conducted openly, with paparazzi pens set up to cover the guests entrance through the hotel main entrance etc), not her private life. Then there was the “bump touching” - again the press were reporting on her actions while in public, not in private. There’s a difference.
The miscarriage was after she and Harry left to live in Los Angeles, at which time the Palace really had no control over what was being written about them, worldwide.