feat(ai-parallel): add Parallel Search integration

[georgeatparallel]

Changes

• Add @tanstack/ai-parallel with a native server-side search tool and typed Parallel Search API client.
• Preserve source citations, application-controlled source policies, cancellation, and search sessions.
• Add integration documentation, focused tests, workspace wiring, and a minor changeset.

Validation

• 18 focused tests, including a real TanStack chat() tool loop.
• Package build, typecheck, lint, formatting, strict package validation, workspace consistency, and documentation links.
• Authenticated Parallel Search API smoke test.

Checklist

• Updated user-facing documentation.
• Included the required minor changeset.

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