refactor(tools/background-task): split tools.ts into focused modules under 200 LOC

- Create modules/ directory with 6 focused modules:
  - background-task.ts: task creation logic
  - background-output.ts: output retrieval logic
  - background-cancel.ts: cancellation logic
  - formatters.ts: message formatting utilities
  - message-processing.ts: message extraction utilities
  - utils.ts: shared utility functions
- Reduce tools.ts from ~798 to ~30 lines (barrel pattern)
- Add new types to types.ts for module interfaces
- Update index.ts for clean re-exports
- Follow modular code architecture (200 LOC limit)

🤖 Generated with assistance of OhMyOpenCode

src/tools/background-task/index.ts

@@ -1,8 +1,8 @@
 export {
+  createBackgroundTask,
   createBackgroundOutput,
   createBackgroundCancel,
 } from "./tools"
 
 export type * from "./types"
 export * from "./constants"
-export type { BackgroundOutputClient, BackgroundOutputManager, BackgroundCancelClient } from "./tools"