docs: add an opt-in stdio bridge example for web research

[georgeatparallel]

Adds an opt-in web research example through CoreCoder's existing stdio MCP loader. The example uses a pinned mcp-remote bridge to reach Parallel Search MCP over Streamable HTTP, with a CoreCoder User-Agent and support for existing network proxy settings.

The setup guide covers Node.js, warming the bridge cache before the 15-second startup timeout, merging the entry into ~/.corecoder/mcp.json, consent and plan mode, one-shot use, and removal. The endpoint is free for light use and needs no Parallel API key. The model still uses the user's existing configuration. Both READMEs link to the example.

Validation:

• 215 tests passed; upstream CI lint scope and compileall passed.
• The installed CLI loaded the exact example in an isolated home. A controlled streaming model fixture drove live anonymous search and fetch calls, returning useful Python TaskGroup documentation and a sourced summary.
• Observed the CoreCoder User-Agent and absence of Authorization on tool discovery, search, and fetch requests. Checked that no configuration retains eight built-in tools and that one-shot mode refuses MCP calls without consent.

The streaming fixture verifies the caller and returned content, rather than autonomous model quality. Unscoped ruff check also reports an existing EXE001 on the unchanged examples/plan_hooks_demo.py; ruff check corecoder tests matches CI and passes.

I work at Parallel. Prepared with AI assistance.