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/session-todo-checker.ts

@@ -0,0 +1,33 @@
+import type { OpencodeClient, Todo } from "./constants"
+
+function isTodo(value: unknown): value is Todo {
+  if (typeof value !== "object" || value === null) return false
+  const todo = value as Record<string, unknown>
+  return (
+    typeof todo["id"] === "string" &&
+    typeof todo["content"] === "string" &&
+    typeof todo["status"] === "string" &&
+    typeof todo["priority"] === "string"
+  )
+}
+
+export async function checkSessionTodos(
+  client: OpencodeClient,
+  sessionID: string
+): Promise<boolean> {
+  try {
+    const response = await client.session.todo({
+      path: { id: sessionID },
+    })
+
+    const todosRaw = "data" in response ? response.data : response
+    if (!Array.isArray(todosRaw) || todosRaw.length === 0) return false
+
+    const incomplete = todosRaw
+      .filter(isTodo)
+      .filter((todo) => todo.status !== "completed" && todo.status !== "cancelled")
+    return incomplete.length > 0
+  } catch {
+    return false
+  }
+}