feat(core): use the same prompt for Search With AFFiNE AI (#12496)

Support [AI-59](https://linear.app/affine-design/issue/AI-59)

Deprecated use of the perplexity model. Makes chat and search use the same prompt content.

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

- **New Features**
  - Added support for two new AI models: Claude Opus 4 and Claude Sonnet 4, enabling enhanced text and image input capabilities.
  - Introduced a new chat prompt with detailed instructions for specialized AI interactions within AFFiNE.

- **Refactor**
  - Improved prompt management for AI chat and search features by centralizing shared settings for better consistency.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

packages/backend/server/src/plugins/copilot/prompt/prompts.ts

@@ -1086,14 +1086,14 @@ Finally, please only send us the content of your continuation in Markdown Format
   },
 ];
 
-const chat: Prompt[] = [
+const CHAT_PROMPT: Omit<Prompt, 'name'> = {
-  {
-    name: 'Chat With AFFiNE AI',
   model: 'gpt-4.1',
   optionalModels: [
     'gpt-4.1',
     'o3',
     'o4-mini',
+    'claude-opus-4-20250514',
+    'claude-sonnet-4-20250514',
     'claude-3-7-sonnet-20250219',
     'claude-3-5-sonnet-20241022',
     'gemini-2.5-flash-preview-05-20',
@@ -1101,7 +1101,7 @@ const chat: Prompt[] = [
     'claude-opus-4@20250514',
     'claude-sonnet-4@20250514',
     'claude-3-7-sonnet@20250219',
-      'claude-3-5-sonnet@20240620',
+    'claude-3-5-sonnet-v2@20241022',
   ],
   messages: [
     {
@@ -1234,11 +1234,16 @@ Below is the user's query. Please respond in the user's preferred language witho
   config: {
     tools: ['webSearch'],
   },
+};
+
+const chat: Prompt[] = [
+  {
+    name: 'Chat With AFFiNE AI',
+    ...CHAT_PROMPT,
   },
   {
     name: 'Search With AFFiNE AI',
-    model: 'sonar-reasoning-pro',
+    ...CHAT_PROMPT,
-    messages: [],
   },
   // use for believer plan
   {

packages/backend/server/src/plugins/copilot/providers/anthropic/official.ts

@@ -15,13 +15,30 @@ export class AnthropicOfficialProvider extends AnthropicProvider<AnthropicOffici
   override readonly type = CopilotProviderType.Anthropic;
 
   override readonly models = [
+    {
+      id: 'claude-opus-4-20250514',
+      capabilities: [
+        {
+          input: [ModelInputType.Text, ModelInputType.Image],
+          output: [ModelOutputType.Text],
+        },
+      ],
+    },
+    {
+      id: 'claude-sonnet-4-20250514',
+      capabilities: [
+        {
+          input: [ModelInputType.Text, ModelInputType.Image],
+          output: [ModelOutputType.Text],
+        },
+      ],
+    },
     {
       id: 'claude-3-7-sonnet-20250219',
       capabilities: [
         {
           input: [ModelInputType.Text, ModelInputType.Image],
           output: [ModelOutputType.Text],
-          defaultForOutputType: true,
         },
       ],
     },
@@ -31,6 +48,7 @@ export class AnthropicOfficialProvider extends AnthropicProvider<AnthropicOffici
         {
           input: [ModelInputType.Text, ModelInputType.Image],
           output: [ModelOutputType.Text],
+          defaultForOutputType: true,
         },
       ],
     },

packages/backend/server/src/plugins/copilot/providers/anthropic/vertex.ts

@@ -41,7 +41,7 @@ export class AnthropicVertexProvider extends AnthropicProvider<AnthropicVertexCo
       ],
     },
     {
-      id: 'claude-3-5-sonnet@20240620',
+      id: 'claude-3-5-sonnet-v2@20241022',
       capabilities: [
         {
           input: [ModelInputType.Text, ModelInputType.Image],