feat: add Tavily as middle-tier search provider alongside Exa

[tavily-integrations]

Summary

Adds Tavily as a configurable search provider that slots in between Exa and SearXNG in the auto provider chain. When Exa is unavailable or quota-exhausted, the system now tries Tavily before falling back to SearXNG.

This is an additive change — all existing Exa functionality and SearXNG fallback behavior is preserved.

Changes

New file: src/searxng_mcp/tavily.py

• TavilySearcher class with has_api_key() guard and async search() method
• Uses AsyncTavilyClient from tavily-python SDK
• Returns standard SearchHit objects, consistent with Exa and SearXNG searchers

Modified: src/searxng_mcp/server.py

• Import and instantiate TavilySearcher
• In unified_search() auto dispatch: added Tavily availability check between Exa and SearXNG
• Added "tavily" as a valid explicit provider option

Modified: src/searxng_mcp/config.py

• Added TAVILY_API_KEY environment variable

Modified: pyproject.toml

• Added tavily-python>=0.5.0 to dependencies

Dependency changes

• Added tavily-python>=0.5.0

Environment variable changes

• Added TAVILY_API_KEY — set to enable Tavily search provider

Notes for reviewers

• Exa remains the highest-priority provider in auto mode; Tavily only activates when Exa is unavailable or exhausted
• The "tavily" provider value can also be used explicitly via SEARCH_PROVIDER=tavily
• exa.py is untouched per the migration plan

Automated Review

• Passed after 1 attempt(s)
• Final review: The exa-provider migration unit correctly implements Tavily as a middle-tier fallback between Exa and SearXNG in the 'auto' provider chain. The TavilySearcher class is well-structured and follows the existing ExaSearcher pattern. The fallback logic in unified_search is correct for all provider modes ("exa", "tavily", "searxng", "auto"). All four files listed in the migration plan are addressed. The Tavily SDK usage (AsyncTavilyClient, response parsing via response.get("results", []), parameter names) is accurate. A few minor issues exist but none are blocking.