Dropdown menu tab button behavior not synced to UI and up / down behavior

[joepio]

Current behavior

• Open a dropdown (e.g. drive switcher)
• Move with tab (nothing happens, no visual indicator, however you can exit the dropdown)
• Move with cursor (see visual indicator move)

Expected behavior

• Tab or down button bevaves the same way
• Focus is synced with arrow selection
• Style set by :focus, just to be sure

[Polleps]

This is intended behaviour

Web application menus are expected to work like desktop application menus. For example, the left and right keys are used to iterate through the top-level items, and the up and down arrows are used to navigate submenus. Pressing the tab key focuses the next item after the menu instead of the next menu item.
w3c.org