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/sessions.py

@@ -8,12 +8,13 @@ from sqlalchemy.orm import selectinload
 from app.dependencies import get_db, get_current_user
 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
 from app.models.user import User
 from app.schemas.session import DailySessionOut, SessionStart, TimerAction
-from app.utils.timer import compute_block_elapsed
+from app.utils.timer import compute_block_elapsed, compute_break_elapsed
 from app.websocket.manager import manager
 
 router = APIRouter(prefix="/api/sessions", tags=["sessions"])
@@ -49,6 +50,8 @@ async def _broadcast_session(db: AsyncSession, session: DailySession) -> None:
                 "duration_minutes": b.duration_minutes,
                 "label": b.label,
                 "order_index": b.order_index,
+                "break_time_enabled": b.break_time_enabled,
+                "break_time_minutes": b.break_time_minutes,
             }
             for b in blocks_result.scalars().all()
         ]
@@ -82,6 +85,15 @@ async def _broadcast_session(db: AsyncSession, session: DailySession) -> None:
         )
         morning_routine = [item.text for item in routine_result.scalars().all()]
 
+    break_activities: list[str] = []
+    if child:
+        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()]
+
     payload = {
         "event": "session_update",
         "session": {
@@ -96,6 +108,7 @@ async def _broadcast_session(db: AsyncSession, session: DailySession) -> None:
         "day_start_time": day_start_time,
         "day_end_time": day_end_time,
         "morning_routine": morning_routine,
+        "break_activities": break_activities,
     }
     await manager.broadcast(session.child_id, payload)
 
@@ -185,6 +198,35 @@ async def timer_action(
     if not session:
         raise HTTPException(status_code=404, detail="Session not found")
 
+    # Break-time events are handled separately — they don't switch blocks or
+    # trigger implicit pauses.  Just record the event and broadcast.
+    BREAK_EVENTS = {"break_start", "break_pause", "break_resume", "break_reset"}
+    if body.event_type in BREAK_EVENTS:
+        block_id = body.block_id or session.current_block_id
+        event = TimerEvent(
+            session_id=session.id,
+            block_id=block_id,
+            event_type=body.event_type,
+        )
+        db.add(event)
+        await db.commit()
+        await db.refresh(session)
+
+        break_elapsed_seconds = 0
+        if body.event_type in ("break_start", "break_reset") and block_id:
+            break_elapsed_seconds, _ = await compute_break_elapsed(db, session.id, block_id)
+
+        ws_payload = {
+            "event": body.event_type,
+            "session_id": session.id,
+            "block_id": block_id,
+            "current_block_id": session.current_block_id,
+            "is_active": session.is_active,
+            "break_elapsed_seconds": break_elapsed_seconds,
+        }
+        await manager.broadcast(session.child_id, ws_payload)
+        return session
+
     # When switching to a different block (start / select / reset), implicitly
     # pause the previous block so the activity log stays accurate.
     prev_block_id = None