docs(web): add Tavily provider documentation

docs/tools/web.md

@@ -1,16 +1,17 @@
 ---
-summary: "Web search + fetch tools (Brave Search API, Perplexity direct/OpenRouter)"
+summary: "Web search + fetch tools (Brave Search API, Perplexity, Tavily)"
 read_when:
   - You want to enable web_search or web_fetch
   - You need Brave Search API key setup
   - You want to use Perplexity Sonar for web search
+  - You want to use Tavily Search for AI-optimized results
 ---
 
 # Web tools
 
 Clawdbot ships two lightweight web tools:
 
-- `web_search` — Search the web via Brave Search API (default) or Perplexity Sonar (direct or via OpenRouter).
+- `web_search` — Search the web via Brave Search API (default), Perplexity Sonar, or Tavily Search.
 - `web_fetch` — HTTP fetch + readable extraction (HTML → markdown/text).
 
 These are **not** browser automation. For JS-heavy sites or logins, use the
@@ -21,6 +22,7 @@ These are **not** browser automation. For JS-heavy sites or logins, use the
 - `web_search` calls your configured provider and returns results.
   - **Brave** (default): returns structured results (title, URL, snippet).
   - **Perplexity**: returns AI-synthesized answers with citations from real-time web search.
+  - **Tavily**: returns high-quality search results optimized for AI applications.
 - Results are cached by query for 15 minutes (configurable).
 - `web_fetch` does a plain HTTP GET and extracts readable content
   (HTML → markdown/text). It does **not** execute JavaScript.
@@ -32,8 +34,7 @@ These are **not** browser automation. For JS-heavy sites or logins, use the
 |----------|------|------|---------|
 | **Brave** (default) | Fast, structured results, free tier | Traditional search results | `BRAVE_API_KEY` |
 | **Perplexity** | AI-synthesized answers, citations, real-time | Requires Perplexity or OpenRouter access | `OPENROUTER_API_KEY` or `PERPLEXITY_API_KEY` |
-
-See [Brave Search setup](/brave-search) and [Perplexity Sonar](/perplexity) for provider-specific details.
+| **Tavily** | AI-optimized results, fast, simple setup | Requires Tavily account | `TAVILY_API_KEY` |
 
 Set the provider in config:
 
@@ -42,7 +43,7 @@ Set the provider in config:
   tools: {
     web: {
       search: {
-        provider: "brave"  // or "perplexity"
+        provider: "brave"  // or "perplexity" or "tavily"
       }
     }
   }
@@ -138,6 +139,40 @@ If no base URL is set, Clawdbot chooses a default based on the API key source:
 | `perplexity/sonar-pro` (default) | Multi-step reasoning with web search | Complex questions |
 | `perplexity/sonar-reasoning-pro` | Chain-of-thought analysis | Deep research |
 
+## Using Tavily
+
+Tavily is a search API built specifically for AI agents. It returns clean, relevant results
+optimized for LLM consumption.
+
+### Getting a Tavily API key
+
+1) Create an account at https://tavily.com/
+2) Generate an API key in your dashboard
+
+Tavily offers a free tier with 1,000 searches/month.
+
+### Setting up Tavily search
+
+```json5
+{
+  tools: {
+    web: {
+      search: {
+        enabled: true,
+        provider: "tavily",
+        tavily: {
+          // API key (optional if TAVILY_API_KEY is set)
+          apiKey: "tvly-..."
+        }
+      }
+    }
+  }
+}
+```
+
+**Environment alternative:** set `TAVILY_API_KEY` in the Gateway environment.
+For a gateway install, put it in `~/.clawdbot/.env`.
+
 ## web_search
 
 Search the web using your configured provider.
@@ -148,6 +183,7 @@ Search the web using your configured provider.
 - API key for your chosen provider:
   - **Brave**: `BRAVE_API_KEY` or `tools.web.search.apiKey`
   - **Perplexity**: `OPENROUTER_API_KEY`, `PERPLEXITY_API_KEY`, or `tools.web.search.perplexity.apiKey`
+  - **Tavily**: `TAVILY_API_KEY` or `tools.web.search.tavily.apiKey`
 
 ### Config