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

packages/shared/src/types/index.ts

@@ -131,3 +131,6 @@ export * from "./auth.types";
 
 // Export widget types
 export * from "./widget.types";
+
+// Export WebSocket types
+export * from "./websocket.types";

packages/shared/src/types/websocket.types.ts

@@ -0,0 +1,87 @@
+/**
+ * WebSocket event types for real-time updates
+ */
+
+/**
+ * All supported WebSocket event names
+ */
+export enum WebSocketEvent {
+  // Task events
+  TASK_CREATED = 'task:created',
+  TASK_UPDATED = 'task:updated',
+  TASK_DELETED = 'task:deleted',
+
+  // Event events
+  EVENT_CREATED = 'event:created',
+  EVENT_UPDATED = 'event:updated',
+  EVENT_DELETED = 'event:deleted',
+
+  // Project events
+  PROJECT_CREATED = 'project:created',
+  PROJECT_UPDATED = 'project:updated',
+  PROJECT_DELETED = 'project:deleted',
+}
+
+/**
+ * Base payload interface for all WebSocket events
+ */
+export interface BaseEventPayload {
+  id: string;
+  workspaceId: string;
+}
+
+/**
+ * Task payload for WebSocket events
+ */
+export interface TaskEventPayload extends BaseEventPayload {
+  title?: string;
+  status?: string;
+  priority?: string;
+  assigneeId?: string | null;
+  projectId?: string | null;
+  dueDate?: string | null;
+  [key: string]: unknown;
+}
+
+/**
+ * Event (calendar) payload for WebSocket events
+ */
+export interface CalendarEventPayload extends BaseEventPayload {
+  title?: string;
+  startTime?: string;
+  endTime?: string;
+  allDay?: boolean;
+  [key: string]: unknown;
+}
+
+/**
+ * Project payload for WebSocket events
+ */
+export interface ProjectEventPayload extends BaseEventPayload {
+  name?: string;
+  status?: string;
+  color?: string;
+  [key: string]: unknown;
+}
+
+/**
+ * Delete payload - only includes the entity ID
+ */
+export interface DeleteEventPayload {
+  id: string;
+}
+
+/**
+ * WebSocket event handler callbacks
+ */
+export interface WebSocketCallbacks {
+  onTaskCreated?: (task: TaskEventPayload) => void;
+  onTaskUpdated?: (task: TaskEventPayload) => void;
+  onTaskDeleted?: (payload: DeleteEventPayload) => void;
+  onEventCreated?: (event: CalendarEventPayload) => void;
+  onEventUpdated?: (event: CalendarEventPayload) => void;
+  onEventDeleted?: (payload: DeleteEventPayload) => void;
+  onProjectCreated?: (project: ProjectEventPayload) => void;
+  onProjectUpdated?: (project: ProjectEventPayload) => void;
+  onProjectDeleted?: (payload: DeleteEventPayload) => void;
+}