feat(web_search): add Volcengine Ark search provider

Add Volcengine (火山引擎) as a new SearchProvider in web_search tool.
Uses Volcengine's Responses API with `tools: [{type: "web_search"}]`
and strict JSON prompt constraints to extract structured search results.

- Free tier: 20K queries/month per API key
- API key resolution: [search] api_key → VOLCENGINE_API_KEY →
  VOLCENGINE_ARK_API_KEY → ARK_API_KEY env vars
- Select via `DEEPSEEK_SEARCH_PROVIDER=volcengine` or
  `[search] provider = "volcengine"` in config.toml

Co-authored-by: Cursor <cursoragent@cursor.com>

config.example.toml

@@ -308,7 +308,7 @@ max_subagents = 10 # optional (1-20)
 # API-backed search.
 #
 # [search]
-# provider = "duckduckgo"  # duckduckgo | bing | tavily | bocha | metaso | baidu
+# provider = "duckduckgo"  # duckduckgo | bing | tavily | bocha | metaso | baidu | volcengine
 #                            # duckduckgo: HTML scrape with Bing fallback
 #                            # bing:       HTML scrape, no API key
 #                            # tavily:     https://tavily.com — AI search, needs api_key
@@ -316,6 +316,8 @@ max_subagents = 10 # optional (1-20)
 #                            # metaso:     https://metaso.cn — 秘塔AI搜索，每天 100 次免费
 #                            #             设置 METASO_API_KEY 或 [search] api_key 可提升额度
 #                            # baidu:      百度 AI Search via qianfan.baidubce.com，需 api_key
+#                            # volcengine: 火山引擎 Ark web_search (免费 2 万次/月), 需 api_key
+#                            #             也回退到 VOLCENGINE_API_KEY / VOLCENGINE_ARK_API_KEY / ARK_API_KEY 环境变量
 # api_key = "YOUR_SEARCH_KEY" # required for tavily, bocha, and baidu; optional for metaso
 #                             # WARNING: treat config.toml like a secret file when
 #                             # storing API keys. Prefer env vars for local smoke tests.