feat: implement structured logging across server components

- Integrated a centralized logging system using createLogger from @automaker/utils, replacing console.log and console.error statements with logger methods for consistent log formatting and improved readability.
- Updated various modules, including auth, events, and services, to utilize the new logging system, enhancing error tracking and operational visibility.
- Refactored logging messages to provide clearer context and information, ensuring better maintainability and debugging capabilities.

This update significantly enhances the observability of the server components, facilitating easier troubleshooting and monitoring.

apps/server/tests/unit/providers/claude-provider.test.ts

@@ -247,10 +247,12 @@ describe('claude-provider.ts', () => {
 
       await expect(collectAsyncGenerator(generator)).rejects.toThrow('SDK execution failed');
 
-      // Should log error with classification info (after refactoring)
+      // Should log error with classification info (via logger)
+      // Logger format: [Context] message, data
       const errorCall = consoleErrorSpy.mock.calls[0];
-      expect(errorCall[0]).toBe('[ClaudeProvider] executeQuery() error during execution:');
-      expect(errorCall[1]).toMatchObject({
+      expect(errorCall[0]).toBe('[ClaudeProvider]');
+      expect(errorCall[1]).toBe('executeQuery() error during execution:');
+      expect(errorCall[2]).toMatchObject({
         type: expect.any(String),
         message: 'SDK execution failed',
         isRateLimit: false,