Yes, click/tap the “+” icon at the bottom of the drop down menu to create new custom sections. it should be right beside the keyboard shortcuts button. to edit sections, click the pencil icon beside the menu section header.
It is for both. As admin you get to see the Make this section public and visible to everyone checkbox at the bottom of the new custom menu section modal. if you don’t enable that, it is your personal menu. if you enable it, it is a global one.
Also, it looks like my menu customizing theme components work in drop down mode (just tested them).
Though this would only update it for those that were still on the default. If they’d changed it/changed it back/made a deliberate choice then it wouldn’t override it as it’s assumed they’ve set it to be how they want it. It tells you how many users it will change it for though, so it gives you a rough idea.
I enabled this component and associated it with a template, but I still don’t see the hamburger menu. I tried different templates to check compatibility. Is there any other recommendation?