✅(frontend) cover presenter divider hint

Exercise hint display, dismissal, and divider detection.

Keep coverage scoped to title-slide guidance.

src/frontend/apps/e2e/__tests__/app-impress/presenter-mode.spec.ts

@@ -15,6 +15,9 @@ import {
   writeInEditor,
 } from './utils-editor';
 
+const dividerHintText =
+  'You can use the divider to tell Docs where to split your slides';
+
 const openPresenter = async (page: Page) => {
   await page.getByLabel('Open the document options').click();
   await page.getByRole('menuitem', { name: 'Present' }).click();
@@ -151,6 +154,36 @@ test.describe('Presenter Mode', () => {
     await expect(overlay).toBeHidden();
   });
 
+  test('shows and dismisses the divider hint on the title slide', async ({
+    page,
+    browserName,
+  }) => {
+    await createDoc(page, 'presenter-divider-hint', browserName, 1);
+    await writeInEditor({ page, text: 'Hello presenter' });
+
+    const overlay = await openPresenter(page);
+
+    await expect(overlay.getByText(dividerHintText)).toBeVisible();
+    await overlay.getByRole('button', { name: /^Close$/ }).click();
+    await expect(overlay.getByText(dividerHintText)).toBeHidden();
+
+    await overlay.getByRole('button', { name: 'Next slide' }).click();
+    await overlay.getByRole('button', { name: 'Previous slide' }).click();
+    await expect(overlay.getByText(dividerHintText)).toBeHidden();
+  });
+
+  test('hides the divider hint when the document already has a divider', async ({
+    page,
+    browserName,
+  }) => {
+    await createDoc(page, 'presenter-divider-hint-hidden', browserName, 1);
+    await writeMultiSlideDoc(page);
+
+    const overlay = await openPresenter(page);
+
+    await expect(overlay.getByText(dividerHintText)).toBeHidden();
+  });
+
   test('moves focus onto the first available control when opened', async ({
     page,
     browserName,

src/frontend/apps/impress/src/features/docs/doc-presenter/__tests__/useSlides.spec.ts

@@ -3,6 +3,7 @@ import { describe, expect, test } from 'vitest';
 import {
   getContentSlideIndexForBlock,
   getSlideTitle,
+  hasDividerBlock,
   splitBlocksIntoSlides,
 } from '../hooks/useSlides';
 
@@ -195,6 +196,23 @@ describe('splitBlocksIntoSlides', () => {
   });
 });
 
+describe('hasDividerBlock', () => {
+  test('returns false when the document has no divider', () => {
+    expect(hasDividerBlock([para('a'), para('b')])).toBe(false);
+  });
+
+  test('detects dividers nested in the block tree', () => {
+    const parent = {
+      ...para('parent'),
+      children: [para('nested'), divider()],
+    };
+
+    expect(hasDividerBlock([para('a'), quote('intro'), para('b')])).toBe(false);
+    expect(hasDividerBlock([para('a'), quote('intro'), divider()])).toBe(true);
+    expect(hasDividerBlock([para('a'), parent])).toBe(true);
+  });
+});
+
 describe('getContentSlideIndexForBlock', () => {
   test('returns the slide containing a regular block', () => {
     expect(