Fix paused timer auto-resuming on page navigation

applySnapshot was always setting isPaused = false and blockStartedAt =
Date.now() regardless of the actual timer state, causing a paused block
to appear running whenever the dashboard was reloaded.

- Add is_paused field to DashboardSnapshot schema
- Dashboard endpoint derives is_paused by checking whether the last
  start/resume/pause event for the current block is a pause
- applySnapshot now reads is_paused from the snapshot instead of
  resetting to false, and only sets blockStartedAt when the block is
  actually running (not paused)

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

backend/app/routers/dashboard.py

@@ -70,7 +70,8 @@ async def get_dashboard(child_id: int, db: AsyncSession = Depends(get_db)):
         )
         completed_ids = [e.block_id for e in events_result.scalars().all() if e.block_id]
 
-    # Compute elapsed seconds for the current block from timer_events
+    # Compute elapsed seconds and paused state for the current block from timer_events
+    is_paused = False
     if session and session.current_block_id:
         tick_result = await db.execute(
             select(TimerEvent)
@@ -93,6 +94,8 @@ async def get_dashboard(child_id: int, db: AsyncSession = Depends(get_db)):
         if last_start:
             elapsed += (datetime.utcnow() - last_start).total_seconds()
         block_elapsed_seconds = int(elapsed)
+        # Paused if the last tick event was a pause (last_start is None but events exist)
+        is_paused = bool(tick_events) and tick_events[-1].event_type == "pause"
 
     return DashboardSnapshot(
         session=session,
@@ -100,6 +103,7 @@ async def get_dashboard(child_id: int, db: AsyncSession = Depends(get_db)):
         blocks=blocks,
         completed_block_ids=completed_ids,
         block_elapsed_seconds=block_elapsed_seconds,
+        is_paused=is_paused,
         day_start_time=day_start_time,
         day_end_time=day_end_time,
     )

backend/app/schemas/session.py

@@ -43,5 +43,6 @@ class DashboardSnapshot(BaseModel):
     blocks: list[ScheduleBlockOut] = []
     completed_block_ids: list[int] = []
     block_elapsed_seconds: int = 0  # seconds already elapsed for the current block
+    is_paused: bool = False          # whether the current block's timer is paused
     day_start_time: time | None = None
     day_end_time: time | None = None