refactor(core): show selected content chip if needed (#13415)

> CLOSE AF-2784

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

## Summary by CodeRabbit

* **Bug Fixes**
* Improved reliability when handling AI chat actions by ensuring valid
context is present before proceeding.
* Enhanced error handling and logging for failed context extraction in
AI chat features.

* **New Features**
* Context extraction is now performed asynchronously before opening the
AI Chat, providing more accurate and relevant chat context.

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

packages/frontend/core/src/blocksuite/ai/components/ai-chat-composer/ai-chat-composer.ts

@@ -211,13 +211,32 @@ export class AIChatComposer extends SignalWatcher(
         if (!params) return;
 
         const { context, host } = params;
-        if (this.host !== host) return;
+        if (this.host !== host || !context) return;
 
-        if (context) {
-          this.updateContext(context);
+        if (
+          context.attachments ||
+          context.snapshot ||
+          context.combinedElementsMarkdown
+        ) {
+          // Wait for context value updated next frame
+          setTimeout(() => {
+            this.addSelectedContextChip().catch(console.error);
+          }, 0);
         }
+      })
+    );
+    this._disposables.add(
+      AIProvider.slots.requestSendWithChat.subscribe(params => {
+        if (!params) return;
 
-        if (context?.attachments) {
+        const { context, host } = params;
+        if (this.host !== host || !context) return;
+
+        if (
+          context.attachments ||
+          context.snapshot ||
+          context.combinedElementsMarkdown
+        ) {
           // Wait for context value updated next frame
           setTimeout(() => {
             this.addSelectedContextChip().catch(console.error);

packages/frontend/core/src/blocksuite/ai/entries/edgeless/actions-config.ts

@@ -52,6 +52,7 @@ import type { AIItemGroupConfig } from '../../components/ai-item/types';
 import { AIProvider } from '../../provider';
 import { getAIPanelWidget } from '../../utils/ai-widgets';
 import { mindMapToMarkdown } from '../../utils/edgeless';
+import { extractSelectedContent } from '../../utils/extract';
 import { canvasToBlob, randomSeed } from '../../utils/image';
 import {
   getCopilotSelectedElems,
@@ -114,11 +115,16 @@ const othersGroup: AIItemGroupConfig = {
       showWhen: () => true,
       handler: host => {
         const panel = getAIPanelWidget(host);
-        AIProvider.slots.requestOpenWithChat.next({
-          host,
-          mode: 'edgeless',
-          autoSelect: true,
-        });
+        extractSelectedContent(host)
+          .then(context => {
+            AIProvider.slots.requestOpenWithChat.next({
+              host,
+              mode: 'edgeless',
+              autoSelect: true,
+              context,
+            });
+          })
+          .catch(console.error);
         panel.hide();
       },
     },