feat(core): add web search tool and reasoning params (#11912)

Close [AI-60](https://linear.app/affine-design/issue/AI-60).

### What changed?
- Add Exa web search tool
- Add reasoning params

packages/backend/server/src/plugins/copilot/tools/index.ts

@@ -0,0 +1 @@
+export * from './web-search';

packages/backend/server/src/plugins/copilot/tools/web-search.ts

@@ -0,0 +1,35 @@
+import { tool } from 'ai';
+import Exa from 'exa-js';
+import { z } from 'zod';
+
+import { Config } from '../../../base';
+
+export const createExaTool = (config: Config) => {
+  return tool({
+    description: 'Search the web for information',
+    parameters: z.object({
+      query: z.string().describe('The query to search the web for.'),
+      mode: z
+        .enum(['MUST', 'CAN'])
+        .optional()
+        .describe('The mode to search the web for.'),
+    }),
+    execute: async ({ query, mode }) => {
+      const { key } = config.copilot.exa;
+      const exa = new Exa(key);
+      const result = await exa.searchAndContents(query, {
+        numResults: 10,
+        summary: true,
+        livecrawl: mode === 'MUST' ? 'always' : undefined,
+      });
+      return result.results.map(data => ({
+        title: data.title,
+        url: data.url,
+        summary: data.summary,
+        favicon: data.favicon,
+        publishedDate: data.publishedDate,
+        author: data.author,
+      }));
+    },
+  });
+};