feat: add Tavily as configurable search provider alongside Brave

[tavily-integrations]

Summary

Adds Tavily Search as a third selectable retrieval endpoint alongside Brave Web Search and LLM Context. Brave remains the default; Tavily activates when a TAVILY_API_KEY is configured.

What changed

• lib/tavily.ts (new): Tavily search module using @tavily/core SDK. Exports tavilySearch() returning the shared RetrievalResult interface, and TavilyError for error handling. Mirrors the shape of lib/brave.ts.
• lib/types.ts: Extended Endpoint type and AnswerRequestSchema to include "tavily".
• lib/env.ts: Added optional TAVILY_API_KEY to the Zod env schema.
• app/api/answer/route.ts: Added tavily branch to retrieval logic with TavilyError handling.
• components/EndpointToggle.tsx: Added third "Tavily" toggle option, updated grid to 3 columns.
• .env.example: Documented TAVILY_API_KEY variable.
• tests/tavily.test.ts (new): Unit tests covering success path, empty results, URL filtering, missing API key, and upstream errors.
• tests/setup.ts: Added test TAVILY_API_KEY default.
• package.json: Added @tavily/core dependency.

Dependency changes

• Added @tavily/core (^0.6.1) to dependencies

Environment variable changes

• Added TAVILY_API_KEY (optional — only required when using the Tavily endpoint)

Notes for reviewers

• Brave endpoints are completely untouched — this is a purely additive change.
• Run pnpm install after checkout to fetch the new @tavily/core dependency.
• The Tavily module creates a new client per request (lightweight); can be optimized to a singleton if needed later.

Automated Review

• Passed after 1 attempt(s)
• Final review: The Tavily provider migration is correct, complete, and non-breaking. All files called out in the plan are present and the implementation faithfully mirrors the shape of lib/brave.ts. The @tavily/core SDK is used correctly (tavily({ apiKey }), client.search with maxResults/searchDepth options), the Endpoint union and AnswerRequestSchema are extended consistently, error handling integrates cleanly into the existing catch-chain, and the UI toggle correctly shifts to a 3-column grid. The only issues are minor: dead/confused code in one test case and a stale JSDoc comment.