feat: add comprehensive logging system with file output

- Add backend logging to logs/backend.log with file rotation support
- Add frontend logging to logs/frontend.log via /api/logs endpoint
- Add frontend logger utility with batching and user context
- Update .gitignore to exclude log files but preserve logs directory
- Update CLAUDE.md with logging documentation and usage examples

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

CLAUDE.md

@@ -21,11 +21,36 @@ Default to using Bun instead of Node.js.
 
 ## Logging
 
-The application uses a custom logger in `src/backend/config.js`:
+The application uses a custom logger that outputs to both files and console.
+
+### Backend Logging
+
+Backend logs are written to `logs/backend.log`:
 - **Log levels**: `debug` (0), `info` (1), `warn` (2), `error` (3)
 - **Default**: `debug` in development, `info` in production
 - **Override**: Set `LOG_LEVEL` environment variable (e.g., `LOG_LEVEL=debug`)
 - **Output format**: `[timestamp] LEVEL: message` with JSON data
+- **Console**: Also outputs to console in development mode
+- **File**: Always writes to `logs/backend.log`
+
+### Frontend Logging
+
+Frontend logs are sent to the backend and written to `logs/frontend.log`:
+- **Logger**: `src/frontend/src/lib/logger.js`
+- **Endpoint**: `POST /api/logs`
+- **Batching**: Batches logs (up to 10 entries or 5 seconds) for performance
+- **User context**: Automatically includes userId and user-agent
+- **Levels**: Same as backend (debug, info, warn, error)
+
+**Usage in frontend**:
+```javascript
+import { logger } from '$lib/logger';
+
+logger.info('User action', { action: 'click', element: 'button' });
+logger.error('API error', { error: err.message });
+logger.warn('Deprecated feature used');
+logger.debug('Component state', { state: componentState });
+```
 
 **Important**: The logger uses the nullish coalescing operator (`??`) to handle log levels. This ensures that `debug` (level 0) is not treated as falsy.
 
@@ -35,6 +60,11 @@ NODE_ENV=development
 LOG_LEVEL=debug
 ```
 
+**Log Files**:
+- `logs/backend.log` - Backend server logs
+- `logs/frontend.log` - Frontend client logs
+- Logs are excluded from git via `.gitignore`
+
 ## Testing
 
 Use `bun test` to run tests.