fix: stabilize the live recommendation path

Co-Authored-By: Claude <noreply@anthropic.com>

frontend/tests/resultPresentation.test.ts

@@ -85,6 +85,48 @@ describe('result presentation', () => {
     expect(onReset).toHaveBeenCalledOnce()
   })
 
+  it('renders demo as a header button and hides logout for a seeded user', () => {
+    const demoUrl = 'https://demo.example.com'
+    const root = mountComponent(AppHeader, {
+      auth: {
+        status: 'authenticated',
+        user: { display_name: 'Seed Listener', can_logout: false },
+        message: null,
+      },
+      mode: 'live',
+      healthFailed: false,
+      demoUrl,
+    })
+    const demoLink = root.querySelector<HTMLAnchorElement>('a.demo-link')
+
+    expect(demoLink?.classList.contains('button')).toBe(true)
+    expect(demoLink?.href).toBe(`${demoUrl}/`)
+    expect(demoLink?.textContent).toContain('demo')
+    expect(root.textContent).toContain('Seed Listener')
+    expect(root.textContent).not.toContain('Log out')
+  })
+
+  it('keeps logout available for an interactive local user', () => {
+    const onLogout = vi.fn()
+    const root = mountComponent(AppHeader, {
+      auth: {
+        status: 'authenticated',
+        user: { display_name: 'Local Listener', can_logout: true },
+        message: null,
+      },
+      mode: 'live',
+      healthFailed: false,
+      demoUrl: null,
+      onLogout,
+    })
+    const logout = [...root.querySelectorAll<HTMLButtonElement>('button')].find((button) =>
+      button.textContent?.includes('Log out'),
+    )
+
+    logout?.click()
+    expect(onLogout).toHaveBeenCalledOnce()
+  })
+
   it('keeps completion context outside the focusable track region', () => {
     const root = mountComponent(AssistantMessage, { turn: doneTurn(), canSave: true })
     const region = root.querySelector<HTMLElement>(