feat: add Brave Search & Baidu Search integration with sub-source support

[YizukiAme]

Summary

Adds Brave Search and Baidu Search as web search providers, with Baidu sub-source configuration (Web Search, Baike, Scholar).

Changes

New Search Providers

• Brave Search: Uses public page scraping — no API key required. Parses Brave's Svelte-rendered HTML to extract search results.
• Baidu Search: Integrates Web Search, Baike (encyclopedia), and Scholar APIs. Users can toggle individual sub-sources on/off.

Provider Icons

• Added icons for Brave (public/icons/brave.png), Baidu (public/icons/baidu.png), and Tavily (public/icons/tavily.jpg)
• Icons displayed in toolbar pill, provider dropdown, and settings sidebar

UI Improvements

• Baidu sub-source toggles use standard Switch components (consistent with rest of the UI)
• Brave API key field shown but marked optional with explanatory notice
• Search toggle enabled when any provider is available (not just selected one)

Technical Details

• lib/web-search/brave.ts: Regex-based HTML parser for Brave's current Svelte-rendered page structure
• lib/web-search/baidu.ts: Accepts subSources parameter, queries enabled sources in parallel
• lib/store/settings.ts: Added baiduSubSources state with per-source toggles
• app/api/web-search/route.ts: Brave bypasses API key check; Baidu passes sub-source config
• components/generation/generation-toolbar.tsx: Fixed webSearchAvailable logic

Files Changed

File	Description
lib/web-search/brave.ts	Fixed HTML parser for current Brave Search structure
lib/web-search/baidu.ts	Added sub-source toggle support
lib/web-search/types.ts	Added BaiduSubSources interface
lib/web-search/constants.ts	Added sub-source config, icon paths
lib/store/settings.ts	Added Baidu sub-source state
app/api/web-search/route.ts	Brave no-key logic, Baidu sub-sources
app/generation-preview/page.tsx	Pass sub-sources in API call
components/settings/web-search-settings.tsx	Sub-source toggles, optional key UI
components/generation/generation-toolbar.tsx	Icons, fixed availability logic
public/icons/*	Provider icons

Testing

• ✅ Baidu Search returns results (verified via API call with key)
• ✅ Brave Search parser matches current HTML structure (tested with saved HTML, 20 results parsed)
• ✅ Build passes (pnpm build exit code 0)
• ✅ UI verified: icons display correctly, search toggle enables properly, Baidu sub-source switches render consistently