Add Parallel as an optional keyless web search provider

What I'd like to contribute

I'm George from Parallel. I'd like to add Parallel as an optional provider in Onyx's existing admin Web Search settings, so users can select it, save the connection without an API key, and use it through the normal Web Search tool.

Our Search MCP at https://search.parallel.ai/mcp supports free anonymous search in Fast mode. It's intended for exploration and light use, with rate limits. This would give users another way to try web search without signing up or running a search server.

Why it could be useful

Artificial Analysis's DeepSearchQA results put Parallel Fast at 80 F1, compared with Tavily Basic at 74. DeepSearchQA tests whether an agent can research across multiple searches and assemble a complete answer, which makes it a useful signal for research tools.

Their time per task chart puts Fast at 18.9 seconds and Tavily Basic at 45.2 seconds, about 58% less time in that benchmark. These are the evaluated API variants, not measurements of Onyx or the proposed MCP adapter. Task time includes measured search time and derived model time.

Proposed design

• Add Parallel to the existing web-search provider types and admin selector. Save the selected provider through the current configuration API and active-provider record.
• Add a small adapter under backend/onyx/tools/tool_implementations/web_search/clients/ using Streamable HTTP MCP. Map web_search results into Onyx's existing WebSearchResult shape, including URLs, titles and relevant excerpts, so the normal search and citation flow can use them.
• Register the adapter in providers.py, allow the keyless connection in the relevant configuration and feature APIs, and make sure the UI only shows it as connected after a provider record has actually been saved.
• Keep provider selection explicit. Leave existing selections, routing and the separate page-content provider behavior intact.
• Explain in setup help that searches send the query to Parallel. Keep stable conversation identifiers for free-tier rate limiting, and follow Onyx's MCP client conventions for attribution, timeouts and errors.

Validation I'd add

I'd test keyless save and activation, provider construction, connection errors and rate limits, result mapping, and invocation through the normal Web Search tool. I'd also check the admin setup flow and run a live anonymous search to verify useful results and citation URLs. None of that implementation validation has run yet.

@yuhongsun96, would you approve this feature and design for a contribution? I'm following the feature and design approval steps in CONTRIBUTING.md before opening a PR.