This article talks about a photo posted by the family’s official X account and how it is probably either photoshopped or ai-generated. They describe multiple red flags in the photo that indicate it has been manipulated. However, it says nothing about Prince William himself releasing the photo.
People magazine and various other sources agree with the claim that the photo was manipulated. https://people.com/kate-middleton-mothers-day-photo-editing-errors-examined-proof-photoshop-found-metadata-8607951
This People article even points out 16 errors pointed out by photoshop experts. But these sources also do not say anything about Prince William releasing the photo personally. So, the claim that the photo is photoshopped, ai-generated, or manipulated in some way is most likely true. The claim that William had anything to do with it is misinformation.