feat: add a hosted keyless search MCP example

• I have looked for existing issues (including closed) about this

Feature Request

Add a small hosted web search example to the existing examples/rmcp package, using Parallel Search MCP through Rig's existing rmcp tool support.

Motivation

The current rmcp example starts a local counter server. A hosted example would show how to discover and call useful remote tools without running a server or setting up model credentials. Parallel's Search MCP offers free, keyless web_search and web_fetch over Streamable HTTP.

I work on developer relations at Parallel and would like to contribute this example.

Proposal

Add examples/rmcp/src/bin/parallel_search.rs and a short entry in the existing examples README. It would connect to https://search.parallel.ai/mcp, discover the tools, call them through Rig's MCP tool adapter, and print search results and fetched excerpts. It would use the workspace's existing rmcp and HTTP dependencies, identify the client as Rig using its package version, and close the connection when finished.

This would be a separate example, leaving the counter example and provider selection as they are. The docs would explain that queries, requested URLs, and supplied context go to Parallel, and that free access has rate limits. Validation would include a focused compile check and an anonymous search and fetch through the example.

Alternatives

Users can already assemble this from rmcp's transport documentation and Rig's counter example. The new example would put the hosted setup and a real search workflow in one runnable place, without adding a provider abstraction or changing Rig's defaults.