Building a custom header/navigation with GenerateBlocks

Yes, You can totally create a header/navigation like that using GB and GPP :)

The button can be added by block element, choose hook as block type, choose generate_menu_bar_item as hook, choose location depends on your needs.

https://docs.generatepress.com/article/block-element-overview/
https://docs.generatepress.com/article/generate_menu_bar_items/

thanks, but I don't see genereate_menu_bar-item as an option.

Have you watched the video in my second link? This is how hook element works.

Easier way is to use block element which can be created at appearance > elements > block element, you can add a Buttons block to the content, and style it using GB.

This is where you can findgenerate_menu_bar_itemin block element.
https://www.screencast.com/t/conRlPSM

Please read the articles I sent to you.