fix(core): input not automatically focused (#10050)

Fix issue [AF-2161](https://linear.app/affine-design/issue/AF-2161).

packages/frontend/core/src/blocksuite/presets/ai/chat-panel/components/add-popover.ts

@@ -7,7 +7,7 @@ import { SignalWatcher, WithDisposable } from '@blocksuite/affine/global/utils';
 import { SearchIcon } from '@blocksuite/icons/lit';
 import type { DocMeta } from '@blocksuite/store';
 import { css, html } from 'lit';
-import { property, state } from 'lit/decorators.js';
+import { property, query, state } from 'lit/decorators.js';
 
 import type { DocSearchMenuConfig } from '../chat-config';
 import type { ChatChip } from '../chat-context';
@@ -93,11 +93,20 @@ export class ChatPanelAddPopover extends SignalWatcher(
   @property({ attribute: false })
   accessor abortController!: AbortController;
 
+  @query('.search-input')
+  accessor searchInput!: HTMLInputElement;
+
   override connectedCallback() {
     super.connectedCallback();
     this._updateDocGroup();
   }
 
+  override firstUpdated() {
+    requestAnimationFrame(() => {
+      this.searchInput.focus();
+    });
+  }
+
   override render() {
     const items = Array.isArray(this._docGroup.items)
       ? this._docGroup.items