fix(ui): show web search providers for all models (#13472)

### What this PR does

Before this PR:
Web search provider options (Tavily, SearXNG, etc.) were only shown for
models matching `isFunctionCallingModel()` or when the user explicitly
set prompt tool-use mode. Local LLM models (e.g. Ollama) showed an empty
web search panel.

After this PR:
Web search provider options are always available for all models.

Fixes #13466

### Why we need it and why it was done in this way

At runtime, models that lack native function-calling support
automatically fall back to prompt-based tool use
(`ApiService.ts:254-256`), so web search providers work regardless of
model capability. The UI gate was unnecessarily restrictive and out of
sync with runtime behavior.

The following tradeoffs were made:
- This removes the UI-level capability check entirely. A discussion
point is whether users should be informed that prompt-based tool use is
being used as a fallback (no visual indicator currently exists).

The following alternatives were considered:
- Matching the gate to the runtime fallback condition
(`isFunctionCallingModel || isToolUseModeFunction`) — rejected because
prompt mode has almost no model restrictions, making any gate
unnecessary.

### Breaking changes

None.

### Special notes for your reviewer

**Behavior change**: selecting a web search provider on a
non-function-calling model now silently triggers prompt-based tool use
at runtime (this fallback already existed but was previously unreachable
from the UI). Please consider whether this implicit fallback is
acceptable or if it needs a user-visible indicator.

### Checklist

- [x] PR: The PR description is expressive enough and will help future
contributors
- [x] Code: Write code that humans can understand and Keep it simple
- [x] Refactor: You have left the code cleaner than you found it (Boy
Scout Rule)
- [ ] Upgrade: Impact of this change on upgrade flows was considered and
addressed if required
- [ ] Documentation: N/A
- [x] Self-review: I have reviewed my own code before requesting review
from others

### Release note

```release-note
Fixed web search provider options not showing for local LLM models (e.g. Ollama) in the chat input toolbar.
```

Signed-off-by: icarus <eurfelux@gmail.com>
Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/renderer/src/pages/home/Inputbar/tools/components/WebSearchQuickPanelManager.tsx

@@ -12,7 +12,6 @@ import {
 import type { QuickPanelListItem } from '@renderer/components/QuickPanel'
 import { QuickPanelReservedSymbol } from '@renderer/components/QuickPanel'
 import {
-  isFunctionCallingModel,
   isGeminiModel,
   isGPT5SeriesReasoningModel,
   isOpenAIWebSearchModel,
@@ -27,7 +26,6 @@ import WebSearchService from '@renderer/services/WebSearchService'
 import { getEffectiveMcpMode, type WebSearchProvider, type WebSearchProviderId } from '@renderer/types'
 import { hasObjectKey } from '@renderer/utils'
 import { isToolUseModeFunction } from '@renderer/utils/assistant'
-import { isPromptToolUse } from '@renderer/utils/mcp-tools'
 import { isGeminiWebSearchProvider } from '@renderer/utils/provider'
 import { Globe } from 'lucide-react'
 import { useCallback, useEffect, useMemo } from 'react'
@@ -138,24 +136,22 @@ export const useWebSearchPanelController = (assistantId: string, quickPanelContr
   const providerItems = useMemo<QuickPanelListItem[]>(() => {
     const isWebSearchModelEnabled = assistant.model && isWebSearchModel(assistant.model)
     const items: QuickPanelListItem[] = []
-    if (isFunctionCallingModel(assistant.model) || isPromptToolUse(assistant)) {
-      items.push(
-        ...providers
-          .map((p) => ({
-            label: p.name,
-            description: WebSearchService.isWebSearchEnabled(p.id)
-              ? hasObjectKey(p, 'apiKey')
-                ? t('settings.tool.websearch.apikey')
-                : t('settings.tool.websearch.free')
-              : t('chat.input.web_search.enable_content'),
-            icon: <WebSearchProviderIcon size={13} pid={p.id} />,
-            isSelected: p.id === assistant?.webSearchProviderId,
-            disabled: !WebSearchService.isWebSearchEnabled(p.id),
-            action: () => updateQuickPanelItem(p.id)
-          }))
-          .filter((item) => !item.disabled)
-      )
-    }
+    items.push(
+      ...providers
+        .map((p) => ({
+          label: p.name,
+          description: WebSearchService.isWebSearchEnabled(p.id)
+            ? hasObjectKey(p, 'apiKey')
+              ? t('settings.tool.websearch.apikey')
+              : t('settings.tool.websearch.free')
+            : t('chat.input.web_search.enable_content'),
+          icon: <WebSearchProviderIcon size={13} pid={p.id} />,
+          isSelected: p.id === assistant?.webSearchProviderId,
+          disabled: !WebSearchService.isWebSearchEnabled(p.id),
+          action: () => updateQuickPanelItem(p.id)
+        }))
+        .filter((item) => !item.disabled)
+    )
 
     if (isWebSearchModelEnabled) {
       items.unshift({