fix(editor): invalid caret in note-edgeless-block on focus (#14229)

### Problem
●In edgeless mode, when starting to edit, `note-block` exhibits two
types of invalid caret behavior:
(1)**Title Region Misalignment**: Clicking on the title region
incorrectly generates the caret in the first line of the note content,
rather than in the title itself.
(2)**Vanishing Caret at Line End**: When clicking in the empty space
beyond the end of a text section, the caret appears momentarily at the
line's end but disappears immediately.
●The following video demonstrates these issues:


https://github.com/user-attachments/assets/db9c2c50-709f-4d32-912c-0f01841d2024


### Solution
●**Title Click Interception**: Added a check to determine if the click
coordinates fall in the title region. If so, the caret positioning is
now handled by a dedicated logic path. Otherwise, it falls back to the
existing note-content logic as before.
●**Range Normalization**: When the generated `range.startContainer` is
not a `TextNode`, try to find a most appropriate `TextNode` and update
the `range` accordingly.

### After
●The video below shows the behavior after this fix.


https://github.com/user-attachments/assets/b2f70b64-1fc6-4049-8379-8bcf3a488a05



<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **Bug Fixes**
* Clicking a page block title no longer creates unwanted paragraphs and
reliably focuses the title.
* Paragraph creation now occurs only when needed and focus is applied
only after successful creation.
* Click coordinates are clamped to container bounds to prevent misplaced
cursors or focus.

* **Improvements**
* Caret normalization: clicks place the caret at the last meaningful
text position for consistent single-cursor behavior.

* **Tests**
  * Added end-to-end coverage for caret placement and focus transitions.
* New ratio-based click/double-click test utilities and a helper for
double-clicking note bodies.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

tests/affine-local/e2e/blocksuite/edgeless/embed.spec.ts

@@ -1,6 +1,7 @@
 import { test } from '@affine-test/kit/playwright';
 import {
   clickEdgelessModeButton,
+  dblclickNoteBody,
   locateEditorContainer,
   locateToolbar,
 } from '@affine-test/kit/utils/editor';
@@ -43,7 +44,7 @@ test('should close embed editing modal when editor switching to page mode by sho
 
 test('embed card should not overflow the edgeless note', async ({ page }) => {
   const note = page.locator('affine-edgeless-note');
-  await note.dblclick();
+  await dblclickNoteBody(page);
   await type(page, '/github');
   await pressEnter(page);
   await page

tests/affine-local/e2e/blocksuite/edgeless/note.spec.ts

@@ -29,6 +29,7 @@ import {
   type,
   waitForEditorLoad,
 } from '@affine-test/kit/utils/page-logic';
+import { clickLocatorByRatio } from '@affine-test/kit/utils/utils';
 import type { EdgelessRootBlockComponent } from '@blocksuite/affine/blocks/root';
 import type { IVec } from '@blocksuite/affine/global/gfx';
 import type { NoteBlockModel } from '@blocksuite/affine/model';
@@ -160,6 +161,59 @@ test.describe('edgeless page block', () => {
     await expect(infoButton).toBeHidden();
   });
 
+  test('caret on focusing', async ({ page }) => {
+    const note = page.locator('affine-edgeless-note');
+    await note.click(); // focus note
+
+    // click on title's rear
+    const docTitle = note.locator('edgeless-page-block-title');
+    await expect(docTitle).toBeVisible();
+    await clickLocatorByRatio(page, docTitle, { xRatio: 0.9, yRatio: 0.8 });
+
+    const hasCaretInTitle = await page.evaluate(
+      hasCaretIn,
+      'edgeless-page-block-title'
+    );
+    expect(hasCaretInTitle).toBe(true);
+
+    await clickLocatorByRatio(page, note, { xRatio: 1.1, yRatio: 0.1 }); // cancel note focus
+    await note.click(); // focus note again
+
+    // click on firstParagraph's rear
+    const firstParagraph = note.locator('affine-paragraph:first-child');
+    await expect(firstParagraph).toBeVisible();
+
+    await clickLocatorByRatio(page, firstParagraph, {
+      xRatio: 0.9,
+      yRatio: 0.5,
+    });
+
+    const hasCaretInParagraph = await page.evaluate(
+      hasCaretIn,
+      'affine-paragraph'
+    );
+    expect(hasCaretInParagraph).toBe(true);
+
+    function hasCaretIn(elemSelector: string) {
+      const sel = document.getSelection();
+      if (!sel || sel.rangeCount === 0) return false;
+
+      const startContainer = sel.getRangeAt(0).startContainer;
+      const selContainer =
+        startContainer.nodeType === Node.TEXT_NODE
+          ? startContainer.parentElement
+          : startContainer;
+
+      if (!selContainer) return false;
+
+      const closestDstElem = (selContainer as HTMLElement)?.closest(
+        elemSelector
+      );
+      if (!closestDstElem) return false;
+      return true;
+    }
+  });
+
   test('page title should be editable', async ({ page }) => {
     const note = page.locator('affine-edgeless-note');
     const docTitle = note.locator('edgeless-page-block-title');

tests/affine-local/e2e/blocksuite/embed/synced.spec.ts

@@ -3,6 +3,7 @@ import {
   clickEdgelessModeButton,
   clickView,
   createEdgelessNoteBlock,
+  dblclickNoteBody,
   fitViewportToContent,
   focusDocTitle,
   getSelectedXYWH,
@@ -35,8 +36,7 @@ test.beforeEach(async ({ page }) => {
 test('should not show hidden note in embed view page mode', async ({
   page,
 }) => {
-  const note = page.locator('affine-edgeless-note');
-  await note.dblclick();
+  await dblclickNoteBody(page);
   await page.keyboard.type('visible content');
   await createEdgelessNoteBlock(page, [100, 100]);
   await page.keyboard.press('Enter');