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/task-queries.ts

@@ -0,0 +1,56 @@
+import type { BackgroundTask } from "./types"
+
+export function getTasksByParentSession(
+  tasks: Iterable<BackgroundTask>,
+  sessionID: string
+): BackgroundTask[] {
+  const result: BackgroundTask[] = []
+  for (const task of tasks) {
+    if (task.parentSessionID === sessionID) {
+      result.push(task)
+    }
+  }
+  return result
+}
+
+export function getAllDescendantTasks(
+  tasksByParent: (sessionID: string) => BackgroundTask[],
+  sessionID: string
+): BackgroundTask[] {
+  const result: BackgroundTask[] = []
+  const directChildren = tasksByParent(sessionID)
+
+  for (const child of directChildren) {
+    result.push(child)
+    if (child.sessionID) {
+      result.push(...getAllDescendantTasks(tasksByParent, child.sessionID))
+    }
+  }
+
+  return result
+}
+
+export function findTaskBySession(
+  tasks: Iterable<BackgroundTask>,
+  sessionID: string
+): BackgroundTask | undefined {
+  for (const task of tasks) {
+    if (task.sessionID === sessionID) return task
+  }
+  return undefined
+}
+
+export function getRunningTasks(tasks: Iterable<BackgroundTask>): BackgroundTask[] {
+  return Array.from(tasks).filter((t) => t.status === "running")
+}
+
+export function getCompletedTasks(tasks: Iterable<BackgroundTask>): BackgroundTask[] {
+  return Array.from(tasks).filter((t) => t.status !== "running")
+}
+
+export function hasRunningTasks(tasks: Iterable<BackgroundTask>): boolean {
+  for (const task of tasks) {
+    if (task.status === "running") return true
+  }
+  return false
+}