feat(core): support gemini model switch in ai (#13631)

<img width="757" height="447" alt="截屏2025-09-22 17 49 34"
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<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- New Features
- Subscription-aware AI model picker in chat: browse models with version
and category, see active selection, switch models, and receive
notifications when choosing pro models without a subscription.
Selections persist across sessions.
- Central AI model service wired into chat UI for consistent model
selection and availability.

- Changes
- Streamlined AI model availability: reduced to a curated set for a more
focused experience.
  - Context menu buttons can display supplemental info next to labels.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

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

@@ -1930,16 +1930,9 @@ Now apply the \`updates\` to the \`content\`, following the intent in \`op\`, an
 const CHAT_PROMPT: Omit<Prompt, 'name'> = {
   model: 'gemini-2.5-flash',
   optionalModels: [
-    'gpt-4.1',
-    'gpt-5',
-    'o3',
-    'o4-mini',
     'gemini-2.5-flash',
     'gemini-2.5-pro',
-    'claude-opus-4@20250514',
     'claude-sonnet-4@20250514',
-    'claude-3-7-sonnet@20250219',
-    'claude-3-5-sonnet-v2@20241022',
   ],
   messages: [
     {
@@ -2099,13 +2092,7 @@ Below is the user's query. Please respond in the user's preferred language witho
       'codeArtifact',
       'blobRead',
     ],
-    proModels: [
-      'gemini-2.5-pro',
-      'claude-opus-4@20250514',
-      'claude-sonnet-4@20250514',
-      'claude-3-7-sonnet@20250219',
-      'claude-3-5-sonnet-v2@20241022',
-    ],
+    proModels: ['gemini-2.5-pro', 'claude-sonnet-4@20250514'],
   },
 };