docs: add TavilyWebSearch component page and external integration entry

integrations/tavily.md

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+---
+layout: integration
+name: Tavily
+description: Search the web using Tavily's AI-powered search API, optimized for LLM applications
+authors:
+    - name: deepset
+      socials:
+        github: deepset-ai
+        twitter: deepset_ai
+        linkedin: https://www.linkedin.com/company/deepset-ai/
+pypi: https://pypi.org/project/tavily-haystack
+repo: https://github.com/deepset-ai/haystack-core-integrations
+type: Search & Extraction
+report_issue: https://github.com/deepset-ai/haystack-core-integrations/issues
+logo: /logos/tavily.png
+version: Haystack 2.0
+toc: true
+---
+
+### Table of Contents
+
+- [Overview](#overview)
+- [Installation](#installation)
+- [Usage](#usage)
+  - [TavilyWebSearch](#tavilywebsearch)
+- [License](#license)
+
+## Overview
+
+[Tavily](https://tavily.com) is an AI-powered search API built for LLM applications. It returns high-quality, structured results with relevant content and source URLs — without the noise of traditional search engines.
+
+This integration provides:
+- [`TavilyWebSearch`](https://docs.haystack.deepset.ai/docs/tavilywebsearch): Searches the web using the Tavily API and returns results as Haystack `Document` objects along with source URLs.
+
+You need a Tavily API key to use this integration. You can get one at [tavily.com](https://tavily.com).
+
+## Installation
+
+```bash
+pip install tavily-haystack
+```
+
+## Usage
+
+### TavilyWebSearch
+
+`TavilyWebSearch` queries the Tavily Search API and returns results as Haystack `Document` objects containing the content snippets and metadata (title, URL). Source URLs are also returned separately.
+
+#### Basic Example
+
+```python
+from haystack_integrations.components.websearch.tavily import TavilyWebSearch
+
+web_search = TavilyWebSearch(top_k=5)
+
+result = web_search.run(query="What is Haystack by deepset?")
+documents = result["documents"]
+links = result["links"]
+```
+
+By default, the component reads the API key from the `TAVILY_API_KEY` environment variable. You can also pass it explicitly:
+
+```python
+from haystack.utils import Secret
+from haystack_integrations.components.websearch.tavily import TavilyWebSearch
+
+web_search = TavilyWebSearch(
+    api_key=Secret.from_token("your-api-key"),
+    top_k=5,
+    search_params={"search_depth": "advanced"},
+)
+```
+
+#### In a Pipeline
+
+Here is an example of a RAG pipeline that uses `TavilyWebSearch` to retrieve web content and answer a question:
+
+```python
+from haystack import Pipeline
+from haystack.utils import Secret
+from haystack.components.builders.chat_prompt_builder import ChatPromptBuilder
+from haystack.components.generators.chat import OpenAIChatGenerator
+from haystack.dataclasses import ChatMessage
+from haystack_integrations.components.websearch.tavily import TavilyWebSearch
+
+web_search = TavilyWebSearch(top_k=3)
+
+prompt_template = [
+    ChatMessage.from_system("You are a helpful assistant."),
+    ChatMessage.from_user(
+        "Given the information below:\n"
+        "{% for document in documents %}{{ document.content }}\n{% endfor %}\n"
+        "Answer the following question: {{ query }}.\nAnswer:",
+    ),
+]
+
+prompt_builder = ChatPromptBuilder(
+    template=prompt_template,
+    required_variables={"query", "documents"},
+)
+
+llm = OpenAIChatGenerator(
+    api_key=Secret.from_env_var("OPENAI_API_KEY"),
+    model="gpt-4o-mini",
+)
+
+pipe = Pipeline()
+pipe.add_component("search", web_search)
+pipe.add_component("prompt_builder", prompt_builder)
+pipe.add_component("llm", llm)
+
+pipe.connect("search.documents", "prompt_builder.documents")
+pipe.connect("prompt_builder.prompt", "llm.messages")
+
+query = "What is Haystack by deepset?"
+result = pipe.run(data={"search": {"query": query}, "prompt_builder": {"query": query}})
+print(result["llm"]["replies"][0].content)
+```
+
+#### Async Support
+
+The component supports asynchronous execution via `run_async`:
+
+```python
+import asyncio
+from haystack_integrations.components.websearch.tavily import TavilyWebSearch
+
+async def main():
+    web_search = TavilyWebSearch(top_k=3)
+    result = await web_search.run_async(query="What is Haystack by deepset?")
+    print(f"Found {len(result['documents'])} documents")
+
+asyncio.run(main())
+```
+
+#### Parameters
+
+- **`api_key`**: API key for Tavily. Defaults to the `TAVILY_API_KEY` environment variable.
+- **`top_k`**: Maximum number of results to return. Defaults to 10.
+- **`search_params`**: Additional parameters passed to the Tavily Search API. Supported keys include `search_depth`, `include_answer`, `include_raw_content`, `include_domains`, `exclude_domains`. See the [Tavily API reference](https://docs.tavily.com/docs/tavily-api/rest_api) for all available options.
+
+### License
+
+`tavily-haystack` is distributed under the terms of the [Apache-2.0](https://spdx.org/licenses/Apache-2.0.html) license.