i) enable the Elements module in Appearance > GenareatePress
ii) Appearance > Elements -> Add New -> Block Element
iii) Select the Hook: menu_bar_items
iv) add whatever you need to the editor
v) set the Display Rules > Location to Entire Site or the locations you require.
NOTE this will appear also on Mobile devices aside of the hamburger icon.
You can use GP hide-on-* classes to remove it if its not required: