fix(editor): hide edgeless only note in synced doc block (#10277)

Closes: [BS-2616](https://linear.app/affine-design/issue/BS-2616/embed-view-%E5%B1%95%E7%A4%BA%E4%B8%8D%E8%AF%A5%E5%87%BA%E7%8E%B0%E7%9A%84-note-%E5%86%85%E5%AE%B9)

blocksuite/blocks/src/root-block/preview/preview-root-block.ts

@@ -1,5 +1,8 @@
+import { NoteBlockModel, NoteDisplayMode } from '@blocksuite/affine-model';
+import { matchModels } from '@blocksuite/affine-shared/utils';
 import { BlockComponent } from '@blocksuite/block-std';
 import { css, html } from 'lit';
+import { repeat } from 'lit/directives/repeat.js';
 
 import { ReadOnlyClipboard } from '../clipboard/readonly-clipboard';
 
@@ -24,8 +27,21 @@ export class PreviewRootBlockComponent extends BlockComponent {
   }
 
   override renderBlock() {
-    return html`<div class="affine-preview-root">
-      ${this.host.renderChildren(this.model)}
-    </div>`;
+    const widgets = html`${repeat(
+      Object.entries(this.widgets),
+      ([id]) => id,
+      ([_, widget]) => widget
+    )}`;
+
+    const children = this.renderChildren(this.model, child => {
+      const isNote = matchModels(child, [NoteBlockModel]);
+      const note = child as NoteBlockModel;
+      const displayOnEdgeless =
+        !!note.displayMode && note.displayMode === NoteDisplayMode.EdgelessOnly;
+      // Should remove deprecated `hidden` property in the future
+      return !(isNote && displayOnEdgeless);
+    });
+
+    return html`<div class="affine-preview-root">${children} ${widgets}</div>`;
   }
 }