My non techie friend experienced the same thing, upgraded to iOS 13, went to see him and he started cursing about "how the f do I save a photo from my messages why the f does Apple got to remove something like that WTF!!!!"
I immediately thought no way they would remove that he must be mistaken, I just upgraded too and hand't tried to do that action. Looked at his phone and sure enough it was gone, tried all sorts of things finally Googled it and oh wow you got to be kidding me scroll down but no indicator you can, that's bad, there is going to be a lot of confused people, why would they do that?