Feature request: Add AgentCore Web Search Tool samples and use case samples

**Description**
Add end-to-end samples demonstrating the AgentCore Web Search Tool connector via AgentCore Gateway, covering setup, agent integration, and advanced multi-turn patterns.

**Motivation**
Customers currently have no runnable examples showing how to:

1. Provision a Gateway with the Web Search connector
2. Integrate it with Strands Agents or LangChain via MCP
3. Build multi-turn research patterns that iterate over search results

Without these samples, customers must piece together documentation and API references on their own.

**Proposed samples:**
Feature samples (01-features/03-connect-your-agent-to-anything/03-web-search/):
Gateway setup (IAM role, Cognito, Gateway, Web Search target)
Raw MCP verification (tools/list + tools/call)
Strands Agents integration
LangChain + LangGraph integration

**PR with implementation: #1645**

Review PR #1645 and the proposed feature-sample directory, 01-features/03-connect-your-agent-to-anything/03-web-search/. Check how the samples cover Gateway setup, raw MCP verification, Strands Agents integration, and LangChain plus LangGraph integration. Done means runnable end-to-end examples demonstrate setup, agent integration, and advanced multi-turn research patterns.

Written by the indexing model from the issue text.