fix(translate,automation): fix schedule import/param errors, add translation schedules to Automation view

- Fix ModuleNotFoundError: 4 lazy imports in _schedule_routes.py changed
  from 3-dot to 4-dot relative imports (src.api.dependencies -> src.dependencies)
- Fix TypeError: update_schedule() param name mismatch (timezone -> timezone_str)
- Add add_translation_job/remove_translation_job to SchedulerService
  to register translation schedules with APScheduler via execute_scheduled_translation
- Add GET /settings/automation/translation-schedules endpoint
  returning all translation schedules with joined job names
- Update Automation settings page to display translation schedules
  (cron, timezone, active badge, last run) below validation policies

backend/src/api/routes/settings.py

@@ -25,7 +25,9 @@ from ...schemas.settings import (
     ValidationPolicyCreate,
     ValidationPolicyUpdate,
     ValidationPolicyResponse,
+    TranslationScheduleItem,
 )
+from ...models.translate import TranslationSchedule, TranslationJob
 from ...core.database import get_db
 from sqlalchemy.orm import Session
 
@@ -598,4 +600,40 @@ async def delete_validation_policy(
 
 # #endregion delete_validation_policy
 
+
+# #region get_translation_schedules [C:2] [TYPE Function]
+# @BRIEF Lists all translation schedules joined with translation job names.
+@router.get("/automation/translation-schedules", response_model=List[TranslationScheduleItem])
+async def get_translation_schedules(
+    db: Session = Depends(get_db),
+    _=Depends(has_permission("admin:settings", "READ")),
+):
+    with belief_scope("get_translation_schedules"):
+        results = (
+            db.query(
+                TranslationSchedule,
+                TranslationJob.name.label("job_name"),
+            )
+            .outerjoin(TranslationJob, TranslationSchedule.job_id == TranslationJob.id)
+            .all()
+        )
+        return [
+            TranslationScheduleItem(
+                schedule_id=ts.id,
+                job_id=ts.job_id,
+                job_name=job_name,
+                cron_expression=ts.cron_expression,
+                timezone=ts.timezone,
+                is_active=ts.is_active,
+                last_run_at=ts.last_run_at,
+                next_run_at=ts.next_run_at,
+                created_by=ts.created_by,
+                created_at=ts.created_at,
+            )
+            for ts, job_name in results
+        ]
+
+
+# #endregion get_translation_schedules
+
 # #endregion SettingsRouter

backend/src/api/routes/translate/_schedule_routes.py

@@ -81,7 +81,7 @@ async def set_schedule(
             schedule = scheduler.update_schedule(
                 job_id,
                 cron_expression=payload.cron_expression,
-                timezone=payload.timezone,
+                timezone_str=payload.timezone,
                 is_active=payload.is_active,
             )
         else:
@@ -92,7 +92,7 @@ async def set_schedule(
                 is_active=payload.is_active,
             )
         # Register with APScheduler via SchedulerService
-        from ...dependencies import get_scheduler_service
+        from ....dependencies import get_scheduler_service
         sched_svc = get_scheduler_service()
         sched_svc.add_translation_job(
             schedule_id=schedule.id,
@@ -133,7 +133,7 @@ async def enable_schedule(
     try:
         scheduler = TranslationScheduler(db, config_manager, current_user.username)
         schedule = scheduler.set_schedule_active(job_id, is_active=True)
-        from ...dependencies import get_scheduler_service
+        from ....dependencies import get_scheduler_service
         sched_svc = get_scheduler_service()
         sched_svc.add_translation_job(
             schedule_id=schedule.id,
@@ -164,7 +164,7 @@ async def disable_schedule(
     try:
         scheduler = TranslationScheduler(db, config_manager, current_user.username)
         scheduler.set_schedule_active(job_id, is_active=False)
-        from ...dependencies import get_scheduler_service
+        from ....dependencies import get_scheduler_service
         sched_svc = get_scheduler_service()
         sched_svc.remove_translation_job(schedule_id=job_id)
         return {"status": "disabled", "job_id": job_id}
@@ -190,7 +190,7 @@ async def delete_schedule(
     try:
         scheduler = TranslationScheduler(db, config_manager, current_user.username)
         scheduler.delete_schedule(job_id)
-        from ...dependencies import get_scheduler_service
+        from ....dependencies import get_scheduler_service
         sched_svc = get_scheduler_service()
         sched_svc.remove_translation_job(schedule_id=job_id)
         return None