fix(editor): drag handle disappeard when hover on the extra area between note and its background (#12536)

Close [BS-3391](https://linear.app/affine-design/issue/BS-3391/无法从note中拖出embed-synced-doc到白板)

### Before
can not hover on drag handle

https://github.com/user-attachments/assets/5596538e-e922-4d7f-8188-b719b234f3ee

### After
can hover on drag handle

https://github.com/user-attachments/assets/855743ec-7601-48a8-8453-cd5aa395bd06

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

## Summary by CodeRabbit

- **Bug Fixes**
	- Improved detection of hovering over notes in edgeless mode, ensuring the drag handle appears correctly when hovering on the background of a selected note.
	- Enhanced background style updates for edgeless notes, providing more accurate visual feedback.

- **Tests**
	- Added a test to verify that the drag handle is visible when hovering over the background of a selected edgeless note.
	- Updated undo/redo tests to improve accuracy of background color evaluation.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

blocksuite/affine/blocks/note/src/components/edgeless-note-background.ts

@@ -26,10 +26,9 @@ import {
 import { GfxControllerIdentifier } from '@blocksuite/std/gfx';
 import type { BlockModel } from '@blocksuite/store';
 import { consume } from '@lit/context';
-import { computed } from '@preact/signals-core';
-import { html, nothing } from 'lit';
+import { computed, effect } from '@preact/signals-core';
+import { nothing } from 'lit';
 import { property } from 'lit/decorators.js';
-import { styleMap } from 'lit/directives/style-map.js';
 
 import { NoteConfigExtension } from '../config';
 import * as styles from './edgeless-note-background.css';
@@ -150,15 +149,20 @@ export class EdgelessNoteBackground extends SignalWatcher(
     return header;
   }
 
+  override connectedCallback() {
+    super.connectedCallback();
+    this.classList.add(styles.background);
+    this.disposables.add(
+      effect(() => {
+        Object.assign(this.style, this.backgroundStyle$.value);
+      })
+    );
+    this.disposables.addFromEvent(this, 'pointerdown', stopPropagation);
+    this.disposables.addFromEvent(this, 'click', this._handleClickAtBackground);
+  }
+
   override render() {
-    return html`<div
-      class=${styles.background}
-      style=${styleMap(this.backgroundStyle$.value)}
-      @pointerdown=${stopPropagation}
-      @click=${this._handleClickAtBackground}
-    >
-      ${this.note.isPageBlock() ? this._renderHeader() : nothing}
-    </div>`;
+    return this.note.isPageBlock() ? this._renderHeader() : nothing;
   }
 
   @consume({ context: stdContext })

blocksuite/affine/widgets/drag-handle/src/utils.ts

@@ -1,7 +1,8 @@
 import { type CalloutBlockComponent } from '@blocksuite/affine-block-callout';
 import {
   AFFINE_EDGELESS_NOTE,
-  type EdgelessNoteBlockComponent,
+  EdgelessNoteBackground,
+  EdgelessNoteBlockComponent,
 } from '@blocksuite/affine-block-note';
 import { ParagraphBlockComponent } from '@blocksuite/affine-block-paragraph';
 import {
@@ -282,14 +283,21 @@ export function getDuplicateBlocks(blocks: BlockModel[]) {
  * Get hovering note with given a point in edgeless mode.
  */
 function getHoveringNote(point: Point) {
-  return (
-    document
-      .elementsFromPoint(point.x, point.y)
-      .find(
-        (e): e is EdgelessNoteBlockComponent =>
-          e.tagName.toLowerCase() === AFFINE_EDGELESS_NOTE
-      ) || null
-  );
+  const elements = document.elementsFromPoint(point.x, point.y);
+  for (const el of elements) {
+    if (el instanceof EdgelessNoteBlockComponent) {
+      return el;
+    }
+
+    // When in edit mode for edgeless-note, the rect of note-background is larger than
+    // that of edgeless-note. Therefore, when the point is located in the area between
+    // note-background and edgeless-note, using elementsFromPoint alone cannot correctly
+    // retrieve the edgeless-note.
+    if (el instanceof EdgelessNoteBackground) {
+      return el.closest(AFFINE_EDGELESS_NOTE) ?? null;
+    }
+  }
+  return null;
 }
 
 export function getSnapshotRect(snapshot: SliceSnapshot): Bound | null {