Refactor offline-first architecture with IndexedDB

Improves dependency injection and service initialization for IndexedDB-based calendar application

Implements lazy initialization for IndexedDB
Fixes race conditions in async event handling
Adds proper dependency injection with registerType
Enhances sync manager and repository pattern

Key improvements:
- Lazy database initialization
- Proper service lifecycle management
- Improved network awareness for sync operations
- Cleaned up initialization logic in index.ts

src/storage/IndexedDBService.ts

@@ -24,6 +24,7 @@ export class IndexedDBService {
   private static readonly SYNC_STATE_STORE = 'syncState';
 
   private db: IDBDatabase | null = null;
+  private initialized: boolean = false;
 
   /**
    * Initialize and open the database
@@ -38,6 +39,7 @@ export class IndexedDBService {
 
       request.onsuccess = () => {
         this.db = request.result;
+        this.initialized = true;
         resolve();
       };
 
@@ -66,6 +68,13 @@ export class IndexedDBService {
     });
   }
 
+  /**
+   * Check if database is initialized
+   */
+  public isInitialized(): boolean {
+    return this.initialized;
+  }
+
   /**
    * Ensure database is initialized
    */