[Feature]: Add Gemini (Google Search grounding) as web_search provider (#13075)

* feat: add Gemini (Google Search grounding) as web_search provider

Add Gemini as a fourth web search provider alongside Brave, Perplexity,
and Grok. Uses Gemini's built-in Google Search grounding tool to return
search results with citations.

- Add runGeminiSearch() with Google Search grounding via tools API
- Resolve Gemini's grounding redirect URLs to direct URLs via parallel
  HEAD requests (5s timeout, graceful fallback)
- Add Gemini config block (apiKey, model) with env var fallback
- Default model: gemini-2.5-flash (fast, cheap, grounding-capable)
- Strip API key from error messages for security
- Add config validation tests for Gemini provider
- Update docs/tools/web.md with Gemini provider documentation

Closes #13074

* feat: auto-detect search provider from available API keys

When no explicit provider is configured, resolveSearchProvider now
checks for available API keys in priority order (Brave → Gemini →
Perplexity → Grok) and selects the first provider with a valid key.

- Add auto-detection logic using existing resolve*ApiKey functions
- Export resolveSearchProvider via __testing_provider for tests
- Add 8 tests covering auto-detection, priority order, and explicit override
- Update docs/tools/web.md with auto-detection documentation

* fix: merge __testing exports, downgrade auto-detect log to debug

* fix: use defaultRuntime.log instead of .debug (not in RuntimeEnv type)

* fix: mark gemini apiKey as sensitive in zod schema

* fix: address Greptile review — add externalContent to Gemini payload, add Gemini/Grok entries to schema labels/help, remove dead schema-fields.ts

* fix(web-search): add JSON parse guard for Gemini API responses

Addresses Greptile review comment: add try/catch to handle non-JSON
responses from Gemini API gracefully, preventing runtime errors on
malformed responses.

Note: FIELD_HELP entries for gemini.apiKey and gemini.model were
already present in schema.help.ts, and gemini.apiKey was already
marked as sensitive in zod-schema.agent-runtime.ts (both fixed in
earlier commits).

* fix: use structured readResponseText result in Gemini error path

readResponseText returns { text, truncated, bytesRead }, not a string.
The Gemini error handler was using the result object directly, which
would always be truthy and never fall through to res.statusText.
Align with Perplexity/xAI/Brave error patterns.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* style: fix import order and formatting after rebase onto main

* Web search: send Gemini API key via header

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
Co-authored-by: Vincent Koc <vincentkoc@ieee.org>

src/config/schema.help.ts

@@ -544,11 +544,17 @@ export const FIELD_HELP: Record<string, string> = {
     'Text suffix for cross-context markers (supports "{channel}").',
   "tools.message.broadcast.enabled": "Enable broadcast action (default: true).",
   "tools.web.search.enabled": "Enable the web_search tool (requires a provider API key).",
-  "tools.web.search.provider": 'Search provider ("brave" or "perplexity").',
+  "tools.web.search.provider":
+    'Search provider ("brave", "perplexity", "grok", or "gemini"). Auto-detected from available API keys if omitted.',
   "tools.web.search.apiKey": "Brave Search API key (fallback: BRAVE_API_KEY env var).",
   "tools.web.search.maxResults": "Default number of results to return (1-10).",
   "tools.web.search.timeoutSeconds": "Timeout in seconds for web_search requests.",
   "tools.web.search.cacheTtlMinutes": "Cache TTL in minutes for web_search results.",
+  "tools.web.search.gemini.apiKey":
+    "Gemini API key for Google Search grounding (fallback: GEMINI_API_KEY env var).",
+  "tools.web.search.gemini.model": 'Gemini model override (default: "gemini-2.5-flash").',
+  "tools.web.search.grok.apiKey": "Grok (xAI) API key (fallback: XAI_API_KEY env var).",
+  "tools.web.search.grok.model": 'Grok model override (default: "grok-3").',
   "tools.web.search.perplexity.apiKey":
     "Perplexity or OpenRouter API key (fallback: PERPLEXITY_API_KEY or OPENROUTER_API_KEY env var).",
   "tools.web.search.perplexity.baseUrl":