- Add POST /api/providers/test endpoint for connection testing with latency and model discovery
- Add provider.dto.ts with TestConnectionDto and TestConnectionResultDto
- Rewrite settings page with full provider management UI: status badges, expandable model tables, capability badges (chat/reasoning/vision), default model indicator, and test connection button with result banner
Fixes#123
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>