Hi there,
that website is real fancy, and i can’t tell you how to replicate that.
However, you can use a Block Element – Hook type in Appearance Elements:
https://docs.generatepress.com/article/block-element-hook/
In the Hook select box you can choose: menu_bar_items
.
And set the Display Rules > Location to Entire Site
or the specific places you want to use.
Whatever you add to the block element editor will now be displayed after the Menu items , on Desktop, Mobile and Sticky Navigation.
If required we can use some CSS to remove the item where it is not required.