Function manage_dialog_lifecycle 

pub fn manage_dialog_lifecycle(
    commands: Commands<'_, '_>,
    tracker: ResMut<'_, FocusTracker>,
    dialogs: Query<'_, '_, (Entity, Option<&Visible>, Option<&mut DialogSession>, Option<&LumenId>, &IfMarker), With<DialogMarker>>,
    children: Query<'_, '_, &Children>,
    parents: Query<'_, '_, &ChildOf>,
    focusables: Query<'_, '_, (&TabIndex, Option<&DocumentOrder>), Without<Disabled>>,
    autofocused: Query<'_, '_, Option<&DocumentOrder>, (With<AutoFocus>, Without<Disabled>)>,
    focus_visibles: Query<'_, '_, (), With<FocusVisible>>,
    live: Query<'_, '_, Entity, Without<IsResource>>,
    closed_out: MessageWriter<'_, DialogClosed>,
)

Qt QDialog lifecycle (W5): initial focus on open, focus restore on close, and the exactly-once accepted/rejected close event.

Open edge (Visible flips true):

• remember the current focus holder,
• focus the first autofocus descendant; else the first focusable (TabIndex >= 0, enabled) descendant in markup order; else the dialog panel itself. The body mounts via deferred commands one tick after the edge, so the pass retries (needs_focus) until a target exists.

Close edge:

• emit exactly one lumen_core::input::DialogClosed - accepted when the default button drove the close (DialogSession::pending_accept), rejected otherwise (Escape, cancel buttons, script writes),
• restore focus to the pre-open holder when focus still sits inside the dialog subtree (a close caused by focusing another widget doesn’t yank focus back) - mirrors lumen_primitives::popup_nav_lifecycle.

The Tab focus trap itself is lumen_input::cycle_focus_on_tab + the FocusBoundary the spawner puts on every <dialog>.