Menu keynav is serious broken

This is the result of 5 minutes of testing the menubar in gtk4-widget-factory:

Opening the menu by clicking on File works as expected. Moving the mouse over Edit and View brings up their menus, and things seem to work fine.

Opening the menu by hitting Alt-F works, but then left/right arrows do not open neighboring menus, as they should. Hitting Alt-E does nothing.

Worse, Alt-F, right arrow, Alt-F makes the menu disappear and starts spewing "Tried to map a grabbing popup with a non-top most parent". At this point, clicking anywhere on the window has no effect anymore.