[Feature]: Add Volcano Engine as a configurable websearch provider

Prerequisites

• I will write this issue in English (see our Language Policy)
• I have searched existing issues and discussions to avoid duplicates
• This feature request is specific to oh-my-opencode (not OpenCode core)
• I have read the documentation or asked an AI coding agent with this project's GitHub URL loaded and couldn't find the answer

Problem Description

Summary

Add Volcano Engine's Web Search API (Volcano Ark) as a third provider option alongside Exa and Tavily.

Motivation

Now that websearch is configurable between Exa and Tavily (#1371), it would be natural to extend the provider list further. Volcano Engine is ByteDance's enterprise AI cloud platform and offers a dedicated Web Search API through Volcano Ark that is well-suited for agent use cases — including structured results, citations, and coverage of real-time data categories like weather, flights, and local services.

Implementation notes

• Volcano Ark's API uses an OpenAI-compatible format, so the adapter should slot in cleanly next to the existing ones in src/mcp/websearch.ts
• Docs: https://www.volcengine.com/docs/82379/1756990

Proposed Solution

Following the same pattern as the existing Exa/Tavily toggle:

{
  "websearch": {
    "provider": "volcengine", // "exa" | "tavily" | "volcengine"
    "volcengine": {
      "api_key": "${VOLCENGINE_API_KEY}"
    }
  }
}

Alternatives Considered

Workaround today: disable the built-in websearch MCP via disabled_mcps and wire up a custom Volcano Engine MCP in .mcp.json. Works, but bypasses the unified provider config.

Doctor Output (Optional)

Additional Context

No response

Feature Type

Configuration Option

Contribution

• I'm willing to submit a PR for this feature
• I can help with testing
• I can help with documentation