Hi Max,
1. You can create a block element, add the button in content area of the block element, set element type to hook, set hook name asmenu_bar_items
, set location to entire site
:
https://docs.generatepress.com/article/block-element-overview/
In this way, the register button will show on mobile without clicking on the menu toggle icon.
2. If you want the button to show after clicking on the menu toggle icon as the other menu items on mobile, then try this method instead:
https://docs.generatepress.com/article/adding-buttons-navigation/