fix(scheduled-tasks): prevent dual-server double dispatch of daily tasks (#2713)

* fix(scheduled-tasks): claim schedule occurrences across server instances

Two OpenChamber servers sharing project config each armed timers and both
dispatched the same daily/weekly/cron/once slot (#2710). Claim the occurrence
in shared config under a cross-process write lock before creating a session.

Co-authored-by: Serhii Dziupin <makeittech@users.noreply.github.com>

* fix(scheduled-tasks): harden occurrence claim failure and lock ownership

Address PR review blockers: release running-slot bookkeeping when claim
throws, avoid silently dropping an armed occurrence after a due-slack sync,
verify lock-file ownership on release, and cover real on-disk lock behavior.

Co-authored-by: Serhii Dziupin <makeittech@users.noreply.github.com>

* fix(scheduled-tasks): always release running slot on state-write failures

Wrap runTask bookkeeping in finally so claim, manual-start, and completion
lock timeouts cannot stuck-run a task; drop the diskNext claim guard that
suppressed later occurrences; recover unparseable locks via mtime age.

Co-authored-by: Serhii Dziupin <makeittech@users.noreply.github.com>

* fix(scheduled-tasks): stop re-arming past nextRunAt and clear stuck running

Only schedule future nextRunAt values so once-task losers and claim-failed
paths cannot spin delay-0 retries. Clear past once nextRunAt on claim, and on
completion-write failure retry terminal status so manual runNow still returns
the session instead of a hard 500 with lastStatus stuck running.

Co-authored-by: Serhii Dziupin <makeittech@users.noreply.github.com>

* fix(scheduled-tasks): release write chain on lock acquire timeout

withProjectWriteLock left the in-process promise chain pending when
acquireProjectFileLock timed out, wedging every later project write and
stranding runTask before finally. Always release the chain; surface
persistError on run; record once claim failures in task state.

Co-authored-by: Serhii Dziupin <makeittech@users.noreply.github.com>

---------

Co-authored-by: Serhii Dziupin <makeittech@users.noreply.github.com>

packages/ui/src/lib/i18n/messages/ko.ts

@@ -237,6 +237,7 @@ export const dict: Record<I18nKey, string> = {
   'sessions.scheduledTasks.dialog.toast.deleted': '예약 작업 삭제됨',
   'sessions.scheduledTasks.dialog.toast.deleteFailed': '작업 삭제 실패',
   'sessions.scheduledTasks.dialog.toast.started': '작업 시작됨',
+  'sessions.scheduledTasks.dialog.toast.startedPersistWarning': '작업은 시작되었지만 상태를 저장하지 못했습니다. 다음 성공 실행까지 계속 실행 중으로 표시될 수 있습니다.',
   'sessions.scheduledTasks.dialog.toast.runFailed': '작업 실행 실패',
   'sessions.scheduledTasks.dialog.confirm.deleteTask': '예약 작업 "{taskName}" 삭제?',
   'sessions.scheduledTasks.dialog.confirm.deleteLoopFile': '루프 작업 "{taskName}" 및 해당 Markdown 파일을 삭제할까요?',