feat: add Tavily search/extract backends to web module

[tavily-integrations]

Summary

• Added TavilySearchBackend and TavilyFetchBackend implementations in a new src/web/backends/tavily.rs module
• TavilySearchBackend uses Tavily's POST /search endpoint to return web search results
• TavilyFetchBackend uses Tavily's POST /extract endpoint for richer content extraction as an alternative to DirectFetchBackend
• Both backends read TAVILY_API_KEY from the environment at call time
• All new code is gated behind a tavily Cargo feature (which implies web)
• DuckDuckGo remains the default; Tavily is opt-in via feature flag and WebContextBuilder

Files changed

• Cargo.toml — Added tavily feature (depends on web), included in full
• src/web/backends/tavily.rs — New file with both backend implementations
• src/web/backends/mod.rs — Feature-gated module declaration and re-exports
• src/web/mod.rs — Feature-gated re-exports of Tavily types

Dependency changes

• No new crate dependencies; Tavily REST API is accessed via the existing reqwest dependency with JSON support

Environment variable changes

• TAVILY_API_KEY — Required at runtime when using TavilySearchBackend or TavilyFetchBackend

Notes for reviewers

• Uses raw reqwest JSON calls to the Tavily REST API rather than a dedicated Tavily crate, keeping the dependency tree minimal
• Follows the same error handling patterns as the existing DuckDuckGo and DirectFetch backends
• Consumers opt in with: WebContextBuilder::new().search(TavilySearchBackend).build()

🤖 Generated with Claude Code

Automated Review

• Passed after 1 attempt(s)
• Final review: The Tavily migration implementation is correct and well-scoped. Both TavilySearchBackend (POST /search) and TavilyFetchBackend (POST /extract) properly implement the existing WebSearchBackend and WebFetchBackend traits with matching signatures. The tavily Cargo feature is correctly additive (enabling web), all four planned files are touched, feature-gating is consistently applied via #[cfg(feature = "tavily")], and DuckDuckGo remains completely untouched. Only minor issues were found — none block approval.