Integrate Claude web search provider and refactor API key resolution

[saif78642]

Summary

Related Issues

Changes

• Added Claude web search provider integration
• Updated AI SDK dependencies (@ai-sdk/anthropic)
• Modified classroom generation logic to support web search
• Updated related configurations and documentation

Type of Change

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update
• Refactoring (no functional changes)
• CI/CD or build changes

Area of Impact

• Classroom generation
• AI/Agent functionality
• Web search integration
• UI/UX
• Infrastructure/DevOps
• Other (please specify)

Verification

Steps to reproduce / test

1. Set up Claude API credentials
2. Navigate to classroom generation settings
3. Select Claude as the web search provider
4. Create a classroom and verify search functionality
5. Test with various search queries and edge cases

What you personally verified

• Web search results are accurate and relevant
• Search integration doesn't break existing classroom generation
• API rate limiting is handled properly
• Error handling for failed searches works correctly
• Performance impact is acceptable

Evidence

Dependencies & Build

• CI passes (pnpm check && pnpm lint && npx tsc --noEmit)
• Updated dependencies (if applicable): @ai-sdk/anthropic, ai, etc.
• No unnecessary dependency changes
• Manually tested locally
• Screenshots / recordings attached (if UI changes)
• E2E tests pass (pnpm test:e2e)

Checklist

• My code follows the project's coding style (TypeScript best practices)
• I have performed a self-review of my code
• I have added/updated documentation as needed
• My changes do not introduce new warnings
• I have tested in both development and production modes
• Updates to dependencies are intentional and documented

[wyuc]

Closing in favor of #393 which covers the same feature with a more complete multi-provider architecture (settings UI, model configurability, SSRF validation, tests). Thanks for the contribution!