Show timer remaining per block and fix single-click block switching

- Block list on both dashboards now shows time remaining on each block's
  timer (allocated duration minus elapsed) instead of total duration;
  the active block counts down live every second
- Fix block switching requiring 2 clicks: replace separate pause+start
  requests with a single start request; backend implicitly records a
  pause event for the previous block atomically
- Export blockElapsedCache from store so views can compute per-block
  elapsed for both running and paused blocks

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

frontend/src/views/DashboardView.vue

@@ -74,6 +74,7 @@
               :block="block"
               :is-current="block.id === scheduleStore.session?.current_block_id"
               :is-completed="scheduleStore.completedBlockIds.includes(block.id)"
+              :elapsed-seconds="blockElapsed(block)"
               @click="selectBlock(block)"
             />
           </div>
@@ -151,9 +152,8 @@ const showStartDialog = ref(false)
 const selectedTemplate = ref(null)
 const templates = ref([])
 
-// Day progress clock (minute precision is enough)
 const now = ref(new Date())
-setInterval(() => { now.value = new Date() }, 60000)
+setInterval(() => { now.value = new Date() }, 1000)
 
 function timeStrToMinutes(str) {
   if (!str) return null
@@ -217,7 +217,15 @@ async function sendAction(type) {
   await scheduleStore.sendTimerAction(scheduleStore.session.id, type)
 }
 
-async function selectBlock(block) {
+function blockElapsed(block) {
+  const currentId = scheduleStore.session?.current_block_id
+  if (block.id === currentId && scheduleStore.blockStartedAt && !scheduleStore.isPaused) {
+    return scheduleStore.blockElapsedOffset + Math.floor((now.value - scheduleStore.blockStartedAt) / 1000)
+  }
+  return scheduleStore.blockElapsedCache[block.id] || 0
+}
+
+function selectBlock(block) {
   if (!scheduleStore.session) return
 
   const currentId = scheduleStore.session.current_block_id
@@ -231,16 +239,8 @@ async function selectBlock(block) {
   // Clicking the current block while running → do nothing
   if (block.id === currentId) return
 
-  // Switching to a different block — pause the current one first if it's running
-  if (currentId && !scheduleStore.isPaused) {
-    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)
+  // Switch to the new block in one atomic step (no separate pause request)
+  scheduleStore.switchBlock(scheduleStore.session.id, block.id)
 }
 
 onMounted(async () => {