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/models/__init__.py

@@ -7,6 +7,7 @@ from app.models.schedule import ScheduleTemplate, ScheduleBlock
 from app.models.session import DailySession, TimerEvent, TimerEventType
 from app.models.activity import ActivityLog
 from app.models.morning_routine import MorningRoutineItem
+from app.models.break_activity import BreakActivityItem
 from app.models.strike import StrikeEvent
 
 __all__ = [
@@ -23,5 +24,6 @@ __all__ = [
     "TimerEventType",
     "ActivityLog",
     "MorningRoutineItem",
+    "BreakActivityItem",
     "StrikeEvent",
 ]

backend/app/models/break_activity.py

@@ -0,0 +1,15 @@
+from sqlalchemy import ForeignKey, Integer, Text
+from sqlalchemy.orm import Mapped, mapped_column, relationship
+
+from app.models.base import Base
+
+
+class BreakActivityItem(Base):
+    __tablename__ = "break_activity_items"
+
+    id: Mapped[int] = mapped_column(primary_key=True, autoincrement=True)
+    user_id: Mapped[int] = mapped_column(ForeignKey("users.id", ondelete="CASCADE"), nullable=False)
+    text: Mapped[str] = mapped_column(Text, nullable=False)
+    order_index: Mapped[int] = mapped_column(Integer, default=0)
+
+    user: Mapped["User"] = relationship("User")  # noqa: F821

backend/app/models/schedule.py

@@ -43,6 +43,8 @@ class ScheduleBlock(Base):
     label: Mapped[str | None] = mapped_column(String(100), nullable=True)  # override subject name
     notes: Mapped[str | None] = mapped_column(Text, nullable=True)
     order_index: Mapped[int] = mapped_column(Integer, default=0)
+    break_time_enabled: Mapped[bool] = mapped_column(Boolean, default=False, nullable=False)
+    break_time_minutes: Mapped[int | None] = mapped_column(Integer, nullable=True)
 
     template: Mapped["ScheduleTemplate"] = relationship("ScheduleTemplate", back_populates="blocks")
     subject: Mapped["Subject | None"] = relationship("Subject", back_populates="schedule_blocks")  # noqa: F821