docs(config): list the DeepSeek search backend in config.example.toml

The DeepSeek Search API shipped as a [search] provider (85688ac230) and is
documented in docs/CONFIGURATION.md, but config.example.toml — the file a user
actually copies — never gained it: the provider list, the description block,
the "needs an api_key" sentence and the api_key comment all stopped at serply.
A reader of the example had no way to discover the backend.

Docs only. `python3 scripts/check-provider-registry.py` passes; the file still
parses as TOML.

Verified separately that the backend itself works: a live
POST https://api.deepseek.com/v1/tools/search returned HTTP 200 with the
documented schema, and a codewhale exec turn with
CODEWHALE_SEARCH_PROVIDER=deepseek returned 5 results through the Web tool with
source="deepseek" in 575 ms. Evidence: CW/artifacts/deepseek-search-20261021/.

config.example.toml

@@ -1016,12 +1016,13 @@ base_url = "https://api.deepseek.com/beta"
 # Choose which backend the Web tool's search uses. Default is keyless Firecrawl
 # (bounded per-IP quota; `[search] api_key` or FIRECRAWL_API_KEY raises it).
 # Bing and DuckDuckGo HTML scraping need no API key. Tavily, Bocha, Metaso,
-# Baidu, Volcengine, Sofya and Serply need an api_key; SearXNG needs base_url.
+# Baidu, Volcengine, Sofya, Serply and DeepSeek need an api_key; SearXNG needs
+# base_url.
 # API runtime failures and empty responses visibly degrade through DuckDuckGo
 # then Bing. Missing configuration and network-policy denials fail closed.
 #
 # [search]
-# provider = "firecrawl"   # firecrawl | bing | duckduckgo | tavily | bocha | metaso | searxng | baidu | volcengine | sofya | serply
+# provider = "firecrawl"   # firecrawl | bing | duckduckgo | tavily | bocha | metaso | searxng | baidu | volcengine | sofya | serply | deepseek
 #                            # firecrawl:  Firecrawl Cloud search, keyless with a bounded per-IP quota
 #                            # duckduckgo: HTML scrape with Bing fallback
 #                            # bing:       HTML scrape, no API key
@@ -1043,9 +1044,13 @@ base_url = "https://api.deepseek.com/beta"
 #                            # serply:     https://serply.io Google organic results with
 #                            #             snippets, needs api_key;
 #                            #             also falls back to the SERPLY_API_KEY env var
+#                            # deepseek:   https://api-docs.deepseek.com/guides/search —
+#                            #             api.deepseek.com/v1/tools/search, needs api_key;
+#                            #             also falls back to the DEEPSEEK_API_KEY env var
+#                            #             (the saved model-provider key is not reused)
 # base_url = "https://search.example/" # optional DuckDuckGo-compatible HTML endpoint;
 #                                      # required SearXNG root or /search endpoint
-# api_key = "YOUR_SEARCH_KEY" # required for tavily, bocha, metaso, baidu, volcengine, sofya, and serply; optional for firecrawl (raises the keyless quota); unused by searxng
+# api_key = "YOUR_SEARCH_KEY" # required for tavily, bocha, metaso, baidu, volcengine, sofya, serply and deepseek; optional for firecrawl (raises the keyless quota); unused by searxng
 #                             # WARNING: treat config.toml like a secret file when
 #                             # storing API keys. Prefer env vars for local smoke tests.
 #