Fix meeting alert catch-up window and skip redundant block switch

- Extend start-time trigger window from 15s to 5 min so opening the
  dashboard late still marks the meeting as started
- Only play chime and show TV overlay when within 30s of start time
- Skip switchBlock call when the session is already on that block

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

frontend/src/composables/useMeetingAlerts.js

@@ -104,17 +104,21 @@ export function useMeetingAlerts(onMeetingStart = null) {
         }
       }
 
-      // At start time: full-screen TV alert, clear dashboard toasts
-      if (secs <= 0 && secs >= -15 && !triggered.has(keyStart)) {
+      // At start time: full-screen TV alert, clear dashboard toasts.
+      // Use a 5-minute catch-up window so opening the dashboard late still triggers.
+      if (secs <= 0 && secs >= -300 && !triggered.has(keyStart)) {
         triggered.add(keyStart)
         dashboardAlerts.value = dashboardAlerts.value.filter(a => a.blockId !== block.id)
-        playChime(false)
-        if (onMeetingStart) onMeetingStart(block.id)
-        tvAlert.value = {
-          blockId: block.id,
-          label: blockLabel(block),
-          autoDismissAt: new Date(Date.now() + 30000),
+        // Only play chime and show TV overlay when meeting just started (within 30s)
+        if (secs >= -30) {
+          playChime(false)
+          tvAlert.value = {
+            blockId: block.id,
+            label: blockLabel(block),
+            autoDismissAt: new Date(Date.now() + 30000),
+          }
         }
+        if (onMeetingStart) onMeetingStart(block.id)
       }
     })
   }, 1000)

frontend/src/views/DashboardView.vue

@@ -283,6 +283,7 @@ const scheduleStore = useScheduleStore()
 const activeChild = computed(() => childrenStore.activeChild)
 const meetingAlerts = useMeetingAlerts((blockId) => {
   if (!scheduleStore.session) return
+  if (scheduleStore.session.current_block_id === blockId) return
   scheduleStore.switchBlock(scheduleStore.session.id, blockId)
 })