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 -->

blocksuite/affine/shared/src/utils/dom/point-to-range.ts

@@ -88,11 +88,73 @@ export function getCurrentNativeRange(selection = window.getSelection()) {
   return selection.getRangeAt(0);
 }
 
+// functions need to be mocked in unit-test
+export const api = {
+  caretRangeFromPoint,
+  resetNativeSelection,
+};
+
 export function handleNativeRangeAtPoint(x: number, y: number) {
-  const range = caretRangeFromPoint(x, y);
+  const range = api.caretRangeFromPoint(x, y);
+  if (range) {
+    normalizeCaretRange(range);
+  }
+
   const startContainer = range?.startContainer;
   // click on rich text
   if (startContainer instanceof Node) {
-    resetNativeSelection(range);
+    api.resetNativeSelection(range);
+  }
+}
+
+function lastMeaningfulTextNode(node: Node) {
+  const walker = document.createTreeWalker(node, NodeFilter.SHOW_TEXT, {
+    acceptNode(node) {
+      return node.textContent && node.textContent?.trim().length > 0
+        ? NodeFilter.FILTER_ACCEPT
+        : NodeFilter.FILTER_REJECT;
+    },
+  });
+
+  let last = null;
+  while (walker.nextNode()) {
+    last = walker.currentNode;
+  }
+  return last;
+}
+
+function normalizeCaretRange(range: Range) {
+  let { startContainer, startOffset } = range;
+  if (startContainer.nodeType === Node.TEXT_NODE) return;
+
+  // Try to find text in the element at `startOffset`
+  const offsetEl =
+    startOffset > 0
+      ? startContainer.childNodes[startOffset - 1]
+      : startContainer.childNodes[0];
+  if (offsetEl) {
+    if (offsetEl.nodeType === Node.TEXT_NODE) {
+      range.setStart(
+        offsetEl,
+        startOffset > 0 ? (offsetEl.textContent?.length ?? 0) : 0
+      );
+      range.collapse(true);
+      return;
+    }
+
+    const text = lastMeaningfulTextNode(offsetEl);
+    if (text) {
+      range.setStart(text, text.textContent?.length ?? 0);
+      range.collapse(true);
+      return;
+    }
+  }
+
+  // Fallback, try to find text in startContainer
+  const text = lastMeaningfulTextNode(startContainer);
+  if (text) {
+    range.setStart(text, text.textContent?.length ?? 0);
+    range.collapse(true);
+    return;
   }
 }