Further to my comment above, I see there was an article last April which reports that Meghan’s letter was sent in response to correspondence from Charles, in which he expressed his sadness over the split within the family.
Yes - the existence of the letters was first revealed in an article Victoria Ward in the Telegraph earlier this year. It was generally taken to have come from he Sussexes as they have often given Victoria stories.
It caused a bit of a furore at the time, and we were told that lawyers on both sides were involved, but the story remained up. So it seems whoever gave Victoria the information had authority to reveal the existence of the letters (if someone, say a staff member, had seen and leaked the contents of private correspondence without permission, I have no doubt the story would have been taken down).
Victoria Ward’s article was also changed quite a lot in the 24 hours or so after it was first published. A sentence in the first version that described the alleged racism incident as something Meghan agreed was an “innocuous comment” and “made without malice” was removed.And a new sentence was added saying how appallingly Meghan and Harry were treated by the Royal family. So it was quite clear who was holding the pen behind the scenes.