I don't think the rumours will stop. People are like a dog with a bone over this. 24 hour social media and news has made them think they deserve every detail. I've read so many comments complaining that "obviously her medical details are private but we should be told what kind of operation or we will keep speculating...."
So, let's imagine (not too hard to imagine from the facts we do know) that Catherine had a bowel resection that went wrong, maybe involving some kind of brief cardiac issue or nasty bacterial infection. Maybe as a result of Crohns or a inflammatory bowel. Maybe you think the public will think its your fault for having an eating disorder when actually your weight had dropped in your most difficult medical flare-ups. Maybe it involved a stoma and colostomy bag, and she needs the months off before a stoma reversal. Women can have abdominal operations that are not hysterectomies. How many here would announce their colostomy bag to the nation? Would you do this if the press have spent years analysing your weight and critiquing/admiring your glamour appearance and wardrobe? Would you appear in public so the Daily Mail could pore over your photos and ask why you were wearing baggy clothing or worse, publishing photos with arrows on, highlighting your stoma bag? And your medication has swollen up your face- it's puffy and swollen- you barely look like you- and you can't face make-up. Would you put out a photo of yourself unphotoshopped? Would you be tempted to lie about how you're currently looking?
The PR around this has been poor but there are plenty of possible reasons why she might want to hide away that are not coma, divorce or overdose.
The only oddity for me was William missing the memorial service but there are so many reasons why that might have happened.
I also think much of the public don't realise Kensington Palace and Buckingham Palace each have their own staff and own approach to publicity. King Charles is an old man with inevitably less vanity over appearance, and his approach has been overall more Frank and public- I think this has been admirable but hasn't helped the Waleses as it is such a contrast to their own highly private approach.
I hope she is doing well, whatever the story is behind the scenes.