fix organize path mapping and task flow

web/src/api/tasks.ts

@@ -8,9 +8,31 @@ export interface ActiveTranscode {
   playlist_ok: boolean
 }
 
+export interface BackgroundTask {
+  id: string
+  kind: string
+  name: string
+  status: 'running' | 'completed' | 'failed'
+  stage?: string
+  source_path?: string
+  dest_path?: string
+  message?: string
+  error?: string
+  metrics?: Record<string, number>
+  started_at: string
+  updated_at: string
+  finished_at?: string
+}
+
+export interface BackgroundTaskSnapshot {
+  active: BackgroundTask[]
+  recent: BackgroundTask[]
+}
+
 export interface TasksSnapshot {
   transcodes: ActiveTranscode[]
   torrents: QBitTorrent[] | null
+  background_tasks?: BackgroundTaskSnapshot
 }
 
 export const tasksAPI = {