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-queue-processor.ts

@@ -0,0 +1,52 @@
+import { log } from "../../shared"
+
+import type { BackgroundTask } from "./types"
+import type { ConcurrencyManager } from "./concurrency"
+
+type QueueItem = {
+  task: BackgroundTask
+  input: import("./types").LaunchInput
+}
+
+export async function processConcurrencyKeyQueue(args: {
+  key: string
+  queuesByKey: Map<string, QueueItem[]>
+  processingKeys: Set<string>
+  concurrencyManager: ConcurrencyManager
+  startTask: (item: QueueItem) => Promise<void>
+}): Promise<void> {
+  const { key, queuesByKey, processingKeys, concurrencyManager, startTask } = args
+
+  if (processingKeys.has(key)) return
+  processingKeys.add(key)
+
+  try {
+    const queue = queuesByKey.get(key)
+    while (queue && queue.length > 0) {
+      const item = queue[0]
+
+      await concurrencyManager.acquire(key)
+
+      if (item.task.status === "cancelled") {
+        concurrencyManager.release(key)
+        queue.shift()
+        continue
+      }
+
+      try {
+        await startTask(item)
+      } catch (error) {
+        log("[background-agent] Error starting task:", error)
+        // Release concurrency slot if startTask failed and didn't release it itself
+        // This prevents slot leaks when errors occur after acquire but before task.concurrencyKey is set
+        if (!item.task.concurrencyKey) {
+          concurrencyManager.release(key)
+        }
+      }
+
+      queue.shift()
+    }
+  } finally {
+    processingKeys.delete(key)
+  }
+}