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/components/ScheduleBlock.vue

@@ -33,6 +33,7 @@ const props = defineProps({
   isCurrent: { type: Boolean, default: false },
   isCompleted: { type: Boolean, default: false },
   compact: { type: Boolean, default: false },
+  elapsedSeconds: { type: Number, default: 0 },
 })
 
 function formatTime(str) {
@@ -46,17 +47,30 @@ function formatTime(str) {
 const subjectColor = computed(() => props.block.subject?.color || '#475569')
 const subjectName = computed(() => props.block.subject?.name || null)
 
-const durationLabel = computed(() => {
-  if (props.block.duration_minutes != null) return `${props.block.duration_minutes} min`
+function blockTotalSeconds() {
+  if (props.block.duration_minutes != null) return props.block.duration_minutes * 60
   const start = props.block.time_start
   const end = props.block.time_end
   if (start && end) {
     const [sh, sm] = start.split(':').map(Number)
     const [eh, em] = end.split(':').map(Number)
-    const mins = (eh * 60 + em) - (sh * 60 + sm)
-    if (mins > 0) return `${mins} min`
+    return ((eh * 60 + em) - (sh * 60 + sm)) * 60
   }
-  return ''
+  return 0
+}
+
+const durationLabel = computed(() => {
+  const totalSec = blockTotalSeconds()
+  if (totalSec <= 0) return ''
+  const remSec = Math.max(0, totalSec - props.elapsedSeconds)
+  const remMin = Math.floor(remSec / 60)
+  if (remMin <= 0) return '0 min'
+  if (remMin >= 60) {
+    const h = Math.floor(remMin / 60)
+    const m = remMin % 60
+    return m === 0 ? `${h}h` : `${h}h ${m}m`
+  }
+  return `${remMin} min`
 })
 </script>