The Save button will still appear whenever you edit your work.
The first time you press Save , you’ll generate a persistent link to your graph.
This means that each time you press Save , the link will stay the same.
So, you can update your graph, and anyone with a link to that graph can reload the page to see your changes without you sending a new link.
There’s also a new look and new folders for saved graphs.
I have an idea of why this is so: Maybe Desmos now stores these locally on your account so you Desmos doesn’t need to update their servers (meaning changing the URL) every time you click ‘Save’.
I think because Desmos hasn’t pushed it’s updates to the app yet. It will take some time… sorry. For now the web-based works better because you can hide the annoying on screen keyboard, and just has a better UI in general.