fix: correctly pass poe web_search via extra_body when built-in search is enabled (#13434)

Fix #13305 

>
https://creator.poe.com/docs/external-applications/openai-compatible-api#using-custom-parameters-with-extra_body

```js
import OpenAI from "openai";

const client = new OpenAI({
    apiKey: process.env.POE_API_KEY,
    baseURL: "https://api.poe.com/v1",
});

// Example: Using web search and thinking level with Gemini models
const response = await client.chat.completions.create({
    model: "Gemini-3-Pro",
    messages: [{ role: "user", content: "What are the latest developments in quantum computing?" }],
    extra_body: {
        web_search: true,
        thinking_level: "high"
    }
});
```

```release-note
fix(poe): correctly pass poe web_search via extra_body when built-in search is enabled
```

src/renderer/src/aiCore/utils/__tests__/options.test.ts

@@ -45,7 +45,8 @@ vi.mock('@cherrystudio/ai-core/provider', async (importOriginal) => {
           'gateway',
           'aihubmix',
           'newapi',
-          'ollama'
+          'ollama',
+          'poe'
         ]
         if (customProviders.includes(id)) {
           return { success: true, data: id }
@@ -433,6 +434,53 @@ describe('options utils', () => {
       })
     })
 
+    describe('Poe provider', () => {
+      const poeProvider: Provider = {
+        id: SystemProviderIds.poe,
+        name: 'Poe',
+        type: 'openai',
+        apiKey: 'test-key',
+        apiHost: 'https://api.poe.com/v1',
+        isSystem: true
+      } as Provider
+
+      const poeModel: Model = {
+        id: 'openai/gpt-4',
+        name: 'GPT-4',
+        provider: SystemProviderIds.poe
+      } as Model
+
+      it('should deep merge Poe extra_body reasoning and web search parameters', async () => {
+        const { getReasoningEffort } = await import('../reasoning')
+        const { getWebSearchParams } = await import('../websearch')
+
+        vi.mocked(getReasoningEffort).mockReturnValue({
+          extra_body: {
+            reasoning_effort: 'medium'
+          }
+        })
+        vi.mocked(getWebSearchParams).mockReturnValue({
+          extra_body: {
+            web_search: true
+          }
+        })
+
+        const result = buildProviderOptions(mockAssistant, poeModel, poeProvider, {
+          enableReasoning: true,
+          enableWebSearch: true,
+          enableGenerateImage: false
+        })
+
+        expect(result.providerOptions).toHaveProperty('poe')
+        expect(result.providerOptions.poe).toMatchObject({
+          extra_body: {
+            reasoning_effort: 'medium',
+            web_search: true
+          }
+        })
+      })
+    })
+
     describe('Custom parameters', () => {
       it('should merge custom provider-specific parameters', async () => {
         const { getCustomParameters } = await import('../reasoning')

src/renderer/src/aiCore/utils/__tests__/websearch.test.ts

@@ -68,6 +68,22 @@ describe('websearch utils', () => {
       })
     })
 
+    it('should return extra_body with web_search for poe provider', () => {
+      const model: Model = {
+        id: 'Gemini-3-Flash',
+        name: 'Gemini 3 Flash',
+        provider: 'poe'
+      } as Model
+
+      const result = getWebSearchParams(model)
+
+      expect(result).toEqual({
+        extra_body: {
+          web_search: true
+        }
+      })
+    })
+
     it('should return empty object for other providers', () => {
       const model: Model = {
         id: 'gpt-4',

src/renderer/src/aiCore/utils/options.ts

@@ -40,6 +40,7 @@ import { type AiSdkParam, isAiSdkParam, type OpenAIVerbosity } from '@renderer/t
 import { isSupportServiceTierProvider, isSupportVerbosityProvider } from '@renderer/utils/provider'
 import type { JSONValue } from 'ai'
 import { t } from 'i18next'
+import { merge } from 'lodash'
 import type { OllamaProviderOptions } from 'ollama-ai-provider-v2'
 
 import { addAnthropicHeaders } from '../prepareParams/header'
@@ -634,10 +635,7 @@ function buildGenericProviderOptions(
 
   if (enableWebSearch) {
     const webSearchParams = getWebSearchParams(model)
-    providerOptions = {
-      ...providerOptions,
-      ...webSearchParams
-    }
+    providerOptions = merge({}, providerOptions, webSearchParams)
   }
 
   // 特殊处理 Qwen MT

src/renderer/src/aiCore/utils/websearch.ts

@@ -25,6 +25,15 @@ export function getWebSearchParams(model: Model): Record<string, any> {
     }
   }
 
+  // https://creator.poe.com/docs/external-applications/openai-compatible-api#using-custom-parameters-with-extra_body
+  if (model.provider === 'poe') {
+    return {
+      extra_body: {
+        web_search: true
+      }
+    }
+  }
+
   if (isOpenAIWebSearchChatCompletionOnlyModel(model)) {
     return {
       web_search_options: {}