feat: cleanup chat panel (#14258)

#### PR Dependency Tree


* **PR #14258** 👈

This tree was auto-generated by
[Charcoal](https://github.com/danerwilliams/charcoal)

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

## Summary by CodeRabbit

## Release Notes

* **Removed Features**
* Web search functionality has been removed from AI chat and related AI
features. Users will no longer see network search options or toggles in
chat preferences and panels.
  * AI chat requests no longer support external web search capabilities.

<sub>✏️ Tip: You can customize this high-level summary in your review
settings.</sub>

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


#### PR Dependency Tree


* **PR #14258** 👈
  * **PR #14259**

This tree was auto-generated by
[Charcoal](https://github.com/danerwilliams/charcoal)

tests/affine-cloud-copilot/e2e/chat-with/network.spec.ts

@@ -10,7 +10,6 @@ test.describe('AIChatWith/Network', () => {
     loggedInPage: page,
     utils,
   }) => {
-    await utils.chatPanel.enableNetworkSearch(page);
     await utils.chatPanel.makeChat(
       page,
       'What is the weather like in Shanghai today?'