fix(cli): address Copilot second-pass review — dialogOpen tick gate, isFocused doc

Two further findings from Copilot:

1. **Interval kept ticking while bg-tasks dialog was open.** The
   first-pass fix already torn the tick down once all rows expired
   from the visibility window, but `dialogOpen` was a separate
   reason the panel returned null and was missed by the gate. Add
   `dialogOpen` to the useEffect deps and short-circuit when true,
   so the dialog's tenure is interval-free.

2. **Stale `isFocused` doc comment in `ToolMessageProps`.** The
   comment claimed the prop controlled the now-retired `Ctrl+E /
   Ctrl+F` display shortcuts (those died with the inline
   `AgentExecutionDisplay` frame). Rewrite the comment to describe
   the only remaining behavior — the focus-routed approval surface
   (focus-holder banner vs. queued-sibling marker).

Coverage delta: +1 case on `LiveAgentPanel.test.tsx` — `tears the
1s tick down when the bg-tasks dialog opens` advances 60s of fake
time with `dialogOpen=true` and asserts no panel state drift.

packages/cli/src/ui/components/background-view/LiveAgentPanel.test.tsx

@@ -295,6 +295,37 @@ describe('<LiveAgentPanel />', () => {
     expect(lastFrame() ?? '').toBe('');
   });
 
+  it('tears the 1s tick down when the bg-tasks dialog opens', () => {
+    // While the dialog is open the panel returns null and the dialog
+    // owns the same data — a still-running interval is a wasted
+    // re-render budget. Verify by checking that advancing the clock
+    // past the visibility window with dialogOpen=true does not flip
+    // the panel into its "expired" state (which would only happen if
+    // the tick advanced `now`).
+    const initial = agentEntry({
+      agentId: 'live-1',
+      subagentType: 'researcher',
+      description: 'researcher: investigate',
+      status: 'completed',
+      startTime: -2000,
+      endTime: 0,
+    });
+    const { config } = makeRegistryConfig([initial]);
+    const { lastFrame } = renderPanel({
+      entries: [initial],
+      config,
+      dialogOpen: true,
+    });
+    // Dialog open → panel hidden, no opportunity for `now` to drift.
+    expect(lastFrame() ?? '').toBe('');
+    act(() => {
+      vi.advanceTimersByTime(60_000);
+    });
+    // Still hidden. The fact that we got here without the panel ever
+    // mounting an interval means subsequent renders won't churn either.
+    expect(lastFrame() ?? '').toBe('');
+  });
+
   it('still shows the snapshot when no Config is mounted (test fixtures)', () => {
     // Without a Config provider the panel can't reach the registry, so
     // it has to trust the snapshot — this is the one place the legacy

packages/cli/src/ui/components/background-view/LiveAgentPanel.tsx

@@ -148,14 +148,20 @@ export const LiveAgentPanel: React.FC<LiveAgentPanelProps> = ({
   const config = useContext(ConfigContext);
 
   // Wall-clock tick. Drives elapsed-time refresh, terminal-row eviction,
-  // AND the live registry re-pull below. The gate must consider both
-  // live agents AND terminal-but-still-visible agents (within the 8s
-  // visibility window) — `BackgroundTaskRegistry.getAll()` retains
-  // terminal entries indefinitely, so a naive `entries.some(isAgentEntry)`
-  // gate would keep ticking forever after the last entry's window
-  // closed, churning re-renders for nothing on screen.
+  // AND the live registry re-pull below. The gate must consider:
+  //   - `dialogOpen` — when the bg-tasks dialog is up, the panel
+  //     renders null (`if (dialogOpen) return null` below), so any
+  //     ticks the interval fires are wasted re-renders.
+  //   - live agents (running / paused) — always need elapsed updates.
+  //   - terminal agents still inside the 8s visibility window — need
+  //     ticks to drive their eviction.
+  // `BackgroundTaskRegistry.getAll()` retains terminal entries
+  // indefinitely, so a naive `entries.some(isAgentEntry)` gate would
+  // keep ticking forever after the last entry's window closed; the
+  // `dialogOpen` arm closes the corresponding gap on the dialog side.
   const [now, setNow] = useState(() => Date.now());
   useEffect(() => {
+    if (dialogOpen) return;
     const needsTick = (whenMs: number) =>
       entries.some((e) => {
         if (!isAgentEntry(e)) return false;
@@ -174,8 +180,7 @@ export const LiveAgentPanel: React.FC<LiveAgentPanelProps> = ({
       if (!needsTick(wallNow)) clearInterval(id);
     }, 1000);
     return () => clearInterval(id);
-     
-  }, [entries]);
+  }, [entries, dialogOpen]);
 
   // Re-pull each agent from the live registry on every tick so the row
   // shows the latest `recentActivities` — `useBackgroundTaskView`

packages/cli/src/ui/components/messages/ToolMessage.tsx

@@ -402,8 +402,13 @@ export interface ToolMessageProps extends IndividualToolCallDisplay {
   config?: Config;
   forceShowResult?: boolean;
   /**
-   * Whether this subagent owns keyboard input for confirmations and
-   * Ctrl+E/Ctrl+F display shortcuts.
+   * Whether this subagent owns keyboard input for the inline approval
+   * surface — when true the focus-holder banner renders and the
+   * underlying ToolConfirmationMessage receives keystrokes; when false
+   * sibling subagents render a dim "Queued approval" marker instead.
+   * (The legacy Ctrl+E / Ctrl+F display shortcuts were retired with
+   * the inline AgentExecutionDisplay frame; LiveAgentPanel owns the
+   * live progress surface and BackgroundTasksDialog owns drill-down.)
    */
   isFocused?: boolean;
   /**