Samsung Browser on Wear OS can now save an image off a webpage. Long-press the picture, tap Download Image, and it lands in the browser's Downloads section. It takes PNG, JPEG, JPG or GIF, and nothing over 10MB. The change was spotted on 30 July.
Desktop browsers have done this since the nineties, and the watch version shipped without it until now. The long-press is for a QR code you need to keep, or a boarding pass you want on your wrist when the phone is dead.