Welcome to Android Central! On my Pixel 3 XL using the Google Messages app, I download photos from a text message by long-pressing the photo, then tapping the Save icon at the top (which looks like a floppy disk -- an odd choice, considering that most smartphone users these days have never seen one of these in real life!). The message I see that shows up is "1 photo saved to Messages album." What this means is that the photo was saved to the /Pictures/Messages directory, and you can see it easily by opening the Google Photos app, swiping in from the left, tapping Device Folders, and looking at the Messages folder.