feat(#16): implement websocket real-time updates

- Add WebSocket gateway with workspace-scoped rooms
- Define event types: task.created, task.updated, task.deleted
- Define event types: event.created, event.updated, event.deleted
- Define event types: project.created, project.updated, project.deleted
- Add shared WebSocket types for type safety
- WebSocketModule already integrated in AppModule

apps/api/src/websocket/websocket.gateway.ts

@@ -135,6 +135,15 @@ export class WebSocketGateway implements OnGatewayConnection, OnGatewayDisconnec
     this.logger.debug(`Emitted event:deleted to ${room}`);
   }
 
+  /**
+   * Emit project:created event to workspace room
+   */
+  emitProjectCreated(workspaceId: string, project: Project): void {
+    const room = this.getWorkspaceRoom(workspaceId);
+    this.server.to(room).emit('project:created', project);
+    this.logger.debug(`Emitted project:created to ${room}`);
+  }
+
   /**
    * Emit project:updated event to workspace room
    */
@@ -144,6 +153,15 @@ export class WebSocketGateway implements OnGatewayConnection, OnGatewayDisconnec
     this.logger.debug(`Emitted project:updated to ${room}`);
   }
 
+  /**
+   * Emit project:deleted event to workspace room
+   */
+  emitProjectDeleted(workspaceId: string, projectId: string): void {
+    const room = this.getWorkspaceRoom(workspaceId);
+    this.server.to(room).emit('project:deleted', { id: projectId });
+    this.logger.debug(`Emitted project:deleted to ${room}`);
+  }
+
   /**
    * Get workspace room name
    */