feat: add Tavily search engine alongside DuckDuckGo and SearXNG

[tavily-integrations]

Summary

• Added Tavily as a third search engine option (additive, parallel to existing providers)
• When TAVILY_API_KEY is set, Tavily is tried first in auto-mode before SearXNG and DuckDuckGo
• Existing DuckDuckGo Lite and SearXNG paths are completely unchanged
• No new Go module dependencies — uses standard net/http + encoding/json

Files changed

• internal/search/tavily.go (new) — TavilyEngine implementing the Engine interface via Tavily REST API
• internal/config/config.go — Added TavilyAPIKey field to SearchConfig
• internal/config/loader.go — Added TAVILY_API_KEY env var override and TavilyAPIKey merge support
• internal/search/search.go — Register Tavily engine at position 0 when key is present; updated engine comments and error message
• cmd/web-search/main.go — Updated --engine flag usage to include tavily; switched to config.Load() for env var support

Environment variable changes

• Added TAVILY_API_KEY — when set, enables the Tavily search engine

Dependency changes

• None — Tavily REST API is called via standard library net/http

Notes for reviewers

• Tavily is inserted at position 0 in the auto-mode engine slice so it is tried first as a higher-quality paid option
• If TAVILY_API_KEY is not set, behavior is identical to before (SearXNG → DuckDuckGo)
• HealthCheck() validates the API key is non-empty; actual API reachability is checked at query time
• The run() function in cmd/web-search/main.go was changed from config.DefaultConfig() to config.Load() so that environment variables are actually applied

🤖 Generated with Claude Code

Automated Review

• Passed after 1 attempt(s)
• Final review: The Tavily migration is correct and well-implemented. The new TavilyEngine properly implements the Engine interface, uses the correct Tavily REST API (POST to https://api.tavily.com/search with Bearer auth), follows existing patterns from searxng.go, and integrates cleanly into the config/loader/search wiring. All five files listed in the plan were modified appropriately. No regressions to existing engines — SearXNG and DDG remain functional with the same relative priority. Two minor issues noted but neither blocks approval.