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/main.py

@@ -9,7 +9,7 @@ from app.config import get_settings
 from app.database import engine
 from app.models import Base
 from app.routers import auth, users, children, subjects, schedules, sessions, logs, dashboard
-from app.routers import morning_routine
+from app.routers import morning_routine, break_activity
 from app.websocket.manager import manager
 
 settings = get_settings()
@@ -33,6 +33,8 @@ async def lifespan(app: FastAPI):
         await _add_column_if_missing(conn, "schedule_templates", "day_start_time", "TIME NULL")
         await _add_column_if_missing(conn, "schedule_templates", "day_end_time", "TIME NULL")
         await _add_column_if_missing(conn, "schedule_blocks", "duration_minutes", "INT NULL")
+        await _add_column_if_missing(conn, "schedule_blocks", "break_time_enabled", "TINYINT(1) NOT NULL DEFAULT 0")
+        await _add_column_if_missing(conn, "schedule_blocks", "break_time_minutes", "INT NULL")
         await _add_column_if_missing(conn, "children", "strikes", "INT NOT NULL DEFAULT 0")
         await _add_column_if_missing(conn, "users", "timezone", "VARCHAR(64) NOT NULL DEFAULT 'UTC'")
     yield
@@ -64,6 +66,7 @@ app.include_router(schedules.router)
 app.include_router(sessions.router)
 app.include_router(logs.router)
 app.include_router(morning_routine.router)
+app.include_router(break_activity.router)
 app.include_router(dashboard.router)