Add Parallel Search docs and update to use python SDK

[NormallyGaussian]

This adds docs for ParallelSearchTool and updates the existing implementation to use the official parallel-web SDK instead of using requests directly. I've also updated the API based on recent changes to the search API.

This is my first PR in this repo, so please let me know if I've missed any steps. Happy to make updates. Thanks!

Note: I did not make any changes to tool.specs.json as the script to generate it made a lot of unrelated changes. Let me know if there's another way to run it.

Tested locally successfully.

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Note

Adds docs and navigation for ParallelSearchTool, migrates the tool to the parallel-web SDK with new config options, and updates tests and dependencies.

• Docs:
  • Add en/tools/search-research/parallelsearchtool page with installation, config, usage, and examples.
  • Link tool in docs.json navigation and search-research/overview.mdx (new card, code snippets import and usage).
• Tool Implementation (parallel_search_tool.py):
  • Replace requests with parallel-web SDK (Parallel().beta.search).
  • New init options: api_key, mode (one-shot/agentic), max_results, excerpts, fetch_policy, source_policy.
  • Runtime params: objective, search_queries, optional overrides for max_results/source_policy.
  • Deprecate processor and max_chars_per_result (mapped via excerpts with warnings).
  • Improved output formatting and env handling (PARALLEL_API_KEY, dotenv).
• Tests:
  • Rewrite to mock SDK, validate param overrides, env/package requirements, and input validation.
• Dependencies:
  • Add optional extra parallel-web>=0.3.4 in pyproject.toml and lockfile entries.
• Tool README:
  • Update usage to SDK-based API, add advanced examples, tips, and deprecation notes.

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