I shouldn’t be able to tab my way out of the menu without closing it. A hamburger menu is kind of a mixture of a menu and a modal, so let’s look at them:
Tabbing my way entirely out of a WAI model will loop back to the top https://www.w3.org/TR/wai-aria-practices-1.1/examples/dialog-modal/dialog.html
Pressing tab while a menu bar submenu is open will close the menu https://www.w3.org/TR/wai-aria-practices-1.1/examples/menubar/menubar-1/menubar-1.html
You should probably do one of these.
Wouldn’t it be fun if, because of the prevalence of the hamburger menu, keyboards started getting a new “hamburger” key? A key that opens the menu of the current context.
Menu keys seeing a new purpose close enough?
My keyboard has a menu key. It even looks like the hamburger menu, with three identical bars in a box, and no mouse cursor.
Pretty good :-)