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>

frontend/src/stores/schedule.js

@@ -35,7 +35,7 @@ export const useScheduleStore = defineStore('schedule', () => {
     session.value = snapshot.session
     blocks.value = sortBlocksByTime(snapshot.blocks)
     completedBlockIds.value = snapshot.completed_block_ids || []
-    isPaused.value = false
+    isPaused.value = snapshot.is_paused || false
     if (snapshot.child) child.value = snapshot.child
     dayStartTime.value = snapshot.day_start_time || null
     dayEndTime.value = snapshot.day_end_time || null
@@ -43,7 +43,8 @@ export const useScheduleStore = defineStore('schedule', () => {
     const serverElapsed = snapshot.block_elapsed_seconds || 0
     if (snapshot.session?.current_block_id && serverElapsed > 0) {
       blockElapsedOffset.value = serverElapsed
-      blockStartedAt.value = Date.now()
+      // Only start the live counter if the block is actually running (not paused)
+      blockStartedAt.value = isPaused.value ? null : Date.now()
     } else {
       blockElapsedOffset.value = 0
       blockStartedAt.value = null