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/break_activity.py

@@ -0,0 +1,97 @@
+from fastapi import APIRouter, Depends, HTTPException, status
+from pydantic import BaseModel
+from sqlalchemy.ext.asyncio import AsyncSession
+from sqlalchemy import select
+
+from app.dependencies import get_db, get_current_user
+from app.models.break_activity import BreakActivityItem
+from app.models.user import User
+
+router = APIRouter(prefix="/api/break-activities", tags=["break-activities"])
+
+
+class BreakActivityItemOut(BaseModel):
+    id: int
+    text: str
+    order_index: int
+    model_config = {"from_attributes": True}
+
+
+class BreakActivityItemCreate(BaseModel):
+    text: str
+    order_index: int = 0
+
+
+class BreakActivityItemUpdate(BaseModel):
+    text: str | None = None
+    order_index: int | None = None
+
+
+@router.get("", response_model=list[BreakActivityItemOut])
+async def list_items(
+    current_user: User = Depends(get_current_user),
+    db: AsyncSession = Depends(get_db),
+):
+    result = await db.execute(
+        select(BreakActivityItem)
+        .where(BreakActivityItem.user_id == current_user.id)
+        .order_by(BreakActivityItem.order_index, BreakActivityItem.id)
+    )
+    return result.scalars().all()
+
+
+@router.post("", response_model=BreakActivityItemOut, status_code=status.HTTP_201_CREATED)
+async def create_item(
+    body: BreakActivityItemCreate,
+    current_user: User = Depends(get_current_user),
+    db: AsyncSession = Depends(get_db),
+):
+    item = BreakActivityItem(user_id=current_user.id, text=body.text, order_index=body.order_index)
+    db.add(item)
+    await db.commit()
+    await db.refresh(item)
+    return item
+
+
+@router.patch("/{item_id}", response_model=BreakActivityItemOut)
+async def update_item(
+    item_id: int,
+    body: BreakActivityItemUpdate,
+    current_user: User = Depends(get_current_user),
+    db: AsyncSession = Depends(get_db),
+):
+    result = await db.execute(
+        select(BreakActivityItem).where(
+            BreakActivityItem.id == item_id,
+            BreakActivityItem.user_id == current_user.id,
+        )
+    )
+    item = result.scalar_one_or_none()
+    if not item:
+        raise HTTPException(status_code=404, detail="Item not found")
+    if body.text is not None:
+        item.text = body.text
+    if body.order_index is not None:
+        item.order_index = body.order_index
+    await db.commit()
+    await db.refresh(item)
+    return item
+
+
+@router.delete("/{item_id}", status_code=status.HTTP_204_NO_CONTENT)
+async def delete_item(
+    item_id: int,
+    current_user: User = Depends(get_current_user),
+    db: AsyncSession = Depends(get_db),
+):
+    result = await db.execute(
+        select(BreakActivityItem).where(
+            BreakActivityItem.id == item_id,
+            BreakActivityItem.user_id == current_user.id,
+        )
+    )
+    item = result.scalar_one_or_none()
+    if not item:
+        raise HTTPException(status_code=404, detail="Item not found")
+    await db.delete(item)
+    await db.commit()