On mobile devices, instead of displaying both the Sign up and Log in buttons, only the Log in button is displayed. Clicking the Log in button opens a modal window that allows users to create a new account, but that might not be obvious to new users, especially if they aren’t familiar with Discourse forums.
So arguably there’s a call to action, but it’s only a call to action for existing users.
The easiest possible fix would be to change the text for the Log in button to “Sign in / Sign up”. The issue is that there’s not a lot of room to play with. This is a quickly made version done with my browser’s dev tools. It would require some adjustments:
Edit: a better but more difficult to implement approach would be to do something similar to what Twitter/X does. On mobile devices, the full Log in and Sign up buttons are displayed in a sticky footer. It’s possible there’s an existing Discourse theme component for this. If not, I suspect it’s something that could be done.