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/stores/schedule.js

@@ -132,6 +132,28 @@ export const useScheduleStore = defineStore('schedule', () => {
     })
   }
 
+  // Switch to a different block in one atomic operation (no separate pause request).
+  // The backend records an implicit pause for the previous block.
+  function switchBlock(sessionId, newBlockId) {
+    if (!session.value) return
+    const prevBlockId = session.value.current_block_id
+
+    // Save elapsed seconds for the block we're leaving
+    if (prevBlockId && blockStartedAt.value) {
+      blockElapsedCache.value[prevBlockId] =
+        blockElapsedOffset.value + Math.floor((Date.now() - blockStartedAt.value) / 1000)
+    }
+
+    // Optimistic update — UI responds immediately
+    session.value.current_block_id = newBlockId
+    isPaused.value = false
+    blockElapsedOffset.value = blockElapsedCache.value[newBlockId] ?? 0
+    blockStartedAt.value = Date.now()
+
+    // Single HTTP call; WS start event will confirm with authoritative elapsed
+    sendTimerAction(sessionId, 'start', newBlockId)
+  }
+
   return {
     session,
     blocks,
@@ -140,6 +162,7 @@ export const useScheduleStore = defineStore('schedule', () => {
     isPaused,
     blockStartedAt,
     blockElapsedOffset,
+    blockElapsedCache,
     dayStartTime,
     dayEndTime,
     currentBlock,
@@ -149,5 +172,6 @@ export const useScheduleStore = defineStore('schedule', () => {
     fetchDashboard,
     startSession,
     sendTimerAction,
+    switchBlock,
   }
 })