fix(home): "next sync" must reflect the schedule the device is *on*

The card's "next sync" was computed locally as `lastSeenAt + interval`,
which broke the moment the user PATCHed a new interval: the device is
still asleep on whatever schedule was active at its last poll, but the
local record now has the new interval, so we'd display a misleading
"in 2m" after a 5→3 min change.

Fix: server stamps `nextPollExpectedAt` on every poll (200/304/204),
PWA reads it directly. The timestamp doesn't move when settings are
edited — only when the device actually polls and picks up a new
schedule. Same field also drives the settings-sheet "Next update"
preview, which had the same flaw.

Side effects:
- `markSeen()` now flushes on the 204 paths too — they previously
  set lastSeenAt without flushing (latent bug for devices with no
  approved images / missing assets).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

frontend/src/views/HomeView.vue

@@ -277,19 +277,38 @@ function nextWakeMatch(times: number[], tz: string): { minutes: number; today: b
   return best
 }
 
+// Prefer the server-stamped nextPollExpectedAt — that's the schedule the
+// device is *actually* on, set every poll. Falls back to a local computation
+// for devices that haven't polled since the column was added.
 function nextSyncLabel(device: Device): string | null {
-  if (device.wakeTimes.length > 0) {
+  let nextMs: number | null = null
+  if (device.nextPollExpectedAt) {
+    nextMs = new Date(device.nextPollExpectedAt).getTime()
+  } else if (device.wakeTimes.length > 0) {
     const next = nextWakeMatch(device.wakeTimes, device.timezone || 'UTC')
     if (!next) return null
     return `next sync ~${formatTime(next.minutes)} ${next.today ? 'today' : 'tomorrow'}`
+  } else if (device.lastSeenAt) {
+    nextMs = new Date(device.lastSeenAt).getTime() + device.rotationIntervalMinutes * 60_000
+  } else {
+    return null
   }
-  if (!device.lastSeenAt) return null
-  const next = new Date(device.lastSeenAt).getTime() + device.rotationIntervalMinutes * 60_000
-  const fromNow = next - Date.now()
+
+  const fromNow = nextMs - Date.now()
   if (fromNow <= 0) return null
   if (fromNow < 60_000)     return 'next sync in <1m'
   if (fromNow < 3_600_000)  return `next sync in ${Math.round(fromNow / 60_000)}m`
-  return `next sync in ${Math.round(fromNow / 3_600_000)}h`
+  if (fromNow < 86_400_000) {
+    // Long horizons read better as a clock time than "in 14h".
+    const tz = device.timezone || 'UTC'
+    const minOfDay = getMinuteOfDayInTz(new Date(nextMs), tz)
+    const dayDelta = daysFromTodayInTz(new Date(nextMs), tz)
+    const dayLabel = dayDelta === 0 ? 'today'
+                   : dayDelta === 1 ? 'tomorrow'
+                   :                  `in ${dayDelta}d`
+    return `next sync ~${formatTime(minOfDay)} ${dayLabel}`
+  }
+  return `next sync in ${Math.round(fromNow / 86_400_000)}d`
 }
 
 // Home shows what's actually on the frame right now — the last image the
@@ -507,17 +526,23 @@ const nextUpdatePreview = computed<string>(() => {
   // The preview is about when the device will *next sync* — it does NOT
   // depend on the proposed new settings, only on the device's current saved
   // schedule. The "no update times yet" hint already lives in the time list.
-  if (!device.lastSeenAt) {
-    return 'Next update: when the frame next connects'
-  }
+  const tz = device.timezone || 'UTC'
 
-  const tz       = device.timezone || 'UTC'
-  const lastSeen = new Date(device.lastSeenAt).getTime()
+  // Prefer the server-stamped expected-next-poll: that timestamp was set
+  // under the schedule active at the device's last poll, and isn't disturbed
+  // by the user's PATCHes — exactly what we want for "when will the new
+  // settings reach the frame?"
   let nextPollMs: number
-  if (device.wakeTimes.length > 0) {
-    nextPollMs = nextWakeAfter(lastSeen, device.wakeTimes, tz)
+  if (device.nextPollExpectedAt) {
+    nextPollMs = new Date(device.nextPollExpectedAt).getTime()
+  } else if (!device.lastSeenAt) {
+    return 'Next update: when the frame next connects'
   } else {
-    nextPollMs = lastSeen + device.rotationIntervalMinutes * 60_000
+    // Legacy fallback for devices that haven't polled since the column was added.
+    const lastSeen = new Date(device.lastSeenAt).getTime()
+    nextPollMs = device.wakeTimes.length > 0
+      ? nextWakeAfter(lastSeen, device.wakeTimes, tz)
+      : lastSeen + device.rotationIntervalMinutes * 60_000
   }
   // Already-overdue device: it'll poll any moment now.
   if (nextPollMs < Date.now()) nextPollMs = Date.now()