Add break time feature to schedule blocks

- Admin: per-block "Break Time" checkbox + duration (min) setting; new
  Break Activities section (global list, same pattern as Morning Routine)
- Dashboard: break timer section appears on blocks with break enabled;
  Start/Pause/Resume/Reset controls work independently of the main timer
- TV: left column switches to amber break badge + countdown during break;
  center column shows configurable Break Activities list
- Backend: break_time_enabled/break_time_minutes columns on schedule_blocks
  (auto-migrated on startup); break_activity_items table + CRUD router;
  break timer events (break_start/pause/resume/reset) stored as TimerEvents
  and broadcast via WebSocket; break_activities included in dashboard
  snapshot and session_update broadcast

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/routers/dashboard.py

@@ -12,6 +12,7 @@ from sqlalchemy.orm import selectinload
 from app.dependencies import get_db
 from app.models.child import Child
 from app.models.morning_routine import MorningRoutineItem
+from app.models.break_activity import BreakActivityItem
 from app.models.schedule import ScheduleBlock, ScheduleTemplate
 from app.models.subject import Subject  # noqa: F401 — needed for selectinload chain
 from app.models.session import DailySession, TimerEvent
@@ -86,6 +87,13 @@ async def get_dashboard(child_id: int, db: AsyncSession = Depends(get_db)):
     )
     morning_routine = [item.text for item in routine_result.scalars().all()]
 
+    break_result = await db.execute(
+        select(BreakActivityItem)
+        .where(BreakActivityItem.user_id == child.user_id)
+        .order_by(BreakActivityItem.order_index, BreakActivityItem.id)
+    )
+    break_activities = [item.text for item in break_result.scalars().all()]
+
     return DashboardSnapshot(
         session=session,
         child=child,
@@ -96,4 +104,5 @@ async def get_dashboard(child_id: int, db: AsyncSession = Depends(get_db)):
         day_start_time=day_start_time,
         day_end_time=day_end_time,
         morning_routine=morning_routine,
+        break_activities=break_activities,
     )