Can't copy photo from text to phone

I have an iPhone 8. Just downloaded iOS 13.1.2, and it seems to be handling photos differently. I got a photo via iMessage. When I tap it, I see the little blue square icon with the arrow pointing up, sort of a "send" button. I click it, as in the past, but no longer see an option to "Save image", which is what would put it on my phone. Now, I see a row of my contacts, sort of shortcuts to text it to, and then a row of apps such as AirDrop, Message, Mail, Messenger, etc. There's also a bar at bottom that says Copy, with an icon sort of 2 documents with the corner folded over to the right, but when I tap on that, nothing seems to happen. Thought it might copy to my phone. Any suggestions? Thanks