Add Linkup as web search provider

[shauryajain21]

This pull request adds Linkup as a web search provider. It follows the same structure as the existing Exa / Tavily / LangSearch providers: it plugs into the web_search fallback chain and the /search provider picker.

Integration

• Added linkupSearch in src/tools/search/linkup.ts, using the official linkup-sdk client (lazily initialized, like exa.ts). It runs a standard-depth search returning 5 results, and uses the shared parseSearchResults / formatToolResult helpers so sourceUrls are populated.
• Registered it in src/tools/registry.ts when LINKUP_API_KEY is set. It is added at the end of the chain, so the default provider order is unchanged.
• Exported it from src/tools/search/index.ts.
• Added a mocked unit test (src/tools/search/linkup.test.ts) that covers request params, URL extraction, and error prefixing.

UI and config

• Added linkup to SearchProviderId / SEARCH_PROVIDERS in src/utils/env.ts and to the provider list in src/components/select-list.ts.
• Added LINKUP_API_KEY to env.example and the README. Keys are available at https://app.linkup.so.

Usage

# .env
LINKUP_API_KEY=your-linkup-api-key

Then pick Linkup with /search to make it the preferred provider. Otherwise it is used as a fallback after the other configured providers.

Tests

• bun run typecheck: passes
• bun test: 319 pass, 0 fail
• Manual live check: web_search returned 5 results with source URLs through the Linkup provider