Fix double-click to switch blocks and TV elapsed reset

Double-click fix:
- After awaiting the pause, optimistically set current_block_id and
  isPaused on the store so the UI switches instantly. The subsequent
  WS start event confirms the state without requiring a second click.

TV elapsed reset fix:
- The TV's local cache was empty for blocks paused before it connected,
  so returning to those blocks showed 0 elapsed.
- Backend now computes the block's accumulated elapsed from previous
  start/pause cycles and includes it as block_elapsed_seconds in the
  'start' WS event payload.
- All clients (Dashboard and TV) now use this authoritative server value
  instead of relying solely on the local cache.

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

frontend/src/stores/schedule.js

@@ -86,9 +86,12 @@ export const useScheduleStore = defineStore('schedule', () => {
       blockStartedAt.value = null
       isPaused.value = true
     }
-    // Start — restore cached elapsed if returning to a previously worked block
+    // Start — use server-provided elapsed (authoritative for all clients incl. TV),
+    // fall back to local cache, then 0 for a fresh block
     if (event.event === 'start') {
-      blockElapsedOffset.value = blockElapsedCache.value[event.block_id] || 0
+      const elapsed = event.block_elapsed_seconds ?? blockElapsedCache.value[event.block_id] ?? 0
+      blockElapsedOffset.value = elapsed
+      if (event.block_id) blockElapsedCache.value[event.block_id] = elapsed
       blockStartedAt.value = Date.now()
       isPaused.value = false
     }

frontend/src/views/DashboardView.vue

@@ -236,6 +236,10 @@ async function selectBlock(block) {
     await scheduleStore.sendTimerAction(scheduleStore.session.id, 'pause', currentId)
   }
 
+  // Optimistically update so the UI switches immediately without waiting for the WS start event
+  scheduleStore.session.current_block_id = block.id
+  scheduleStore.isPaused = false
+
   scheduleStore.sendTimerAction(scheduleStore.session.id, 'start', block.id)
 }