manager: always close idle pipe when sending ready notification

This fixes a bug introduced by 6d932659.

The commit makes several functions skipped if the manager is already
in finished state, as
> In manager_check_finished(), more steps are skipped if MANAGER_IS_FINISHED().
> Those steps are idempotent, but no need to waste cycles trying to do them
> more than once.

However, the idle pipe may be re-opened after manager is finished:
manager_dispatch_run_queue() -> manager_watch_idle_pipe().
So, the closing the pipe is not idempotent here.

Fixes #21889.

(cherry picked from commit 9c1b17c3)