fix: Prefer model-provided web search result count over admin default (open-webui#22577)

* Prefer model-provided web search result count over admin default

Update `search_web` to prioritize the model-provided `count` parameter before falling back to the admin-configured `WEB_SEARCH_RESULT_COUNT`, and finally defaulting to 5.

Changes:
- Set `count` default to `None` instead of `5`.
- Adjust fallback order to: model-provided `count` → admin-configured value → `5`.
- Update comment to reflect the new precedence logic.

This ensures explicit model requests for result count are respected while preserving sensible defaults.

* Enforce maximum web search result count from config

Update `search_web` to cap the model-provided `count` parameter at the admin-configured `WEB_SEARCH_RESULT_COUNT` to prevent excessive result requests.

Changes:
- Set default `count` parameter to `5`.
- Replace fallback logic with enforcement logic that limits `count` to the configured maximum.
- Update comment to reflect that the result count is now capped to prevent abuse.

This ensures web search requests cannot exceed the configured limit while maintaining a sensible default.

Author: Steve-Li-1998

backend/open_webui/tools/builtin.py

@@ -168,8 +168,8 @@ async def search_web(
         engine = __request__.app.state.config.WEB_SEARCH_ENGINE
         user = UserModel(**__user__) if __user__ else None
 
-        # Use admin-configured result count if configured, falling back to model-provided count of provided, else default to 5
-        count = __request__.app.state.config.WEB_SEARCH_RESULT_COUNT or count
+        # Enforce maximum result count from config to prevent abuse
+        count = count if count < __request__.app.state.config.WEB_SEARCH_RESULT_COUNT else __request__.app.state.config.WEB_SEARCH_RESULT_COUNT
 
         results = await asyncio.to_thread(_search_web, __request__, engine, query, user)