feat: add Tavily search provider to packages/core

[tavily-integrations]

Summary

Adds Tavily as a configurable search provider alongside the existing Exa AI search service in packages/core. This is an additive (parallel) migration — no existing Exa functionality is modified or removed.

Changes

• New file: packages/core/src/service/tavily-search.ts — Implements TavilySearchService with a static search() method using the official @tavily/core SDK. Mirrors the ExaSearchService interface pattern (static method returning Promise<string>).
• packages/core/src/service/index.ts — Added TavilySearchService export.
• packages/core/src/index.ts — Added TavilySearchService to the main barrel export.
• packages/core/src/service/chat-service.ts — Extended the websearch options type with provider?: "exa" | "tavily" so callers can specify which search backend to use.
• packages/core/package.json — Added @tavily/core as a runtime dependency.

Dependency changes

• Added @tavily/core: ^0.6.1 to packages/core/package.json dependencies

Environment variable changes

• TAVILY_API_KEY — required when using TavilySearchService (passed as apiKey parameter)

Notes for reviewers

• Existing ExaSearchService and all its exports remain completely untouched.
• The provider field on websearch options is optional and defaults behavior is unchanged.
• Callers need to pass a Tavily API key explicitly to TavilySearchService.search().

Automated Review

• Passed after 1 attempt(s)
• Final review: The additive Tavily migration for the core package is well-implemented. All five files identified in the plan are correctly modified. The @tavily/core SDK is used correctly (tavily({ apiKey }) + client.search()), TavilySearchService mirrors the ExaSearchService interface (static search() → Promise<string>), the provider discriminator field is properly optional in ChatService.websearch (no regressions), and exports are wired through both barrel files and the main package index. Two minor gaps: no timeout guard (ExaSearchService uses 25 s), and the TAVILY_API_KEY env var noted in the migration plan is not documented anywhere (no .env.example update).