refactor(background-agent): split manager.ts into focused modules

Extract 30+ single-responsibility modules from manager.ts (1556 LOC):
- task lifecycle: task-starter, task-completer, task-canceller, task-resumer
- task queries: task-queries, task-poller, task-queue-processor
- notifications: notification-builder, notification-tracker, parent-session-notifier
- session handling: session-validator, session-output-validator, session-todo-checker
- spawner: spawner/ directory with focused spawn modules
- utilities: duration-formatter, error-classifier, message-storage-locator
- result handling: result-handler-context, background-task-completer
- shutdown: background-manager-shutdown, process-signal

src/features/background-agent/format-duration.ts

@@ -0,0 +1,14 @@
+export function formatDuration(start: Date, end?: Date): string {
+  const duration = (end ?? new Date()).getTime() - start.getTime()
+  const seconds = Math.floor(duration / 1000)
+  const minutes = Math.floor(seconds / 60)
+  const hours = Math.floor(minutes / 60)
+
+  if (hours > 0) {
+    return `${hours}h ${minutes % 60}m ${seconds % 60}s`
+  }
+  if (minutes > 0) {
+    return `${minutes}m ${seconds % 60}s`
+  }
+  return `${seconds}s`
+}