refactor(features/background-agent): remove dead code submodules

Delete 15 unused files in background-agent module:

- background-task-completer.ts

- format-duration.ts

- message-dir.ts

- parent-session-context-resolver.ts

- parent-session-notifier.ts (and its test file)

- result-handler-context.ts

- result-handler.ts

- session-output-validator.ts

- session-task-cleanup.ts

- session-todo-checker.ts

- spawner/background-session-creator.ts

- spawner/concurrency-key-from-launch-input.ts

- spawner/spawner-context.ts

- spawner/tmux-callback-invoker.ts

Update index.ts barrel and manager.ts/spawner.ts imports

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-opencode)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/features/background-agent/spawner.ts

@@ -61,9 +61,7 @@ export async function startTask(
   const createResult = await client.session.create({
     body: {
       parentID: input.parentSessionID,
-      title: `Background: ${input.description}`,
-    // eslint-disable-next-line @typescript-eslint/no-explicit-any
-    } as any,
+    } as Record<string, unknown>,
     query: {
       directory: parentDirectory,
     },