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

[wyuc]

Thanks for the contribution, and sorry for the long delay on my side.

This PR is now quite far behind main and conflicts with the current web-search architecture, so it is not mergeable as-is. There are also a few areas that would need another look after an update, including how the new providers plug into the current searchWeb flow, server-side classroom generation, Baidu sub-source handling, and test coverage for the Brave parser.

If you’re still interested in maintaining this PR, please rebase it onto the latest main and adapt it to the current web-search provider architecture. I’ll be happy to review it again after that.

[YizukiAme]

Got it! I'll rebase this onto main and update the code to fit the current architecture in a couple of days when I have some bandwidth.
Thanks for the review~