[feat](client): surface expiry, endings, and device health in the app

The alert detail screen now creates with a lifetime (1/3/7/14 days) and shows expiresAt, lists subscriber rows by their non-identifying fields, and renders each ending (delivered, expired, disarmed, deleted) as a terminal state instead of a stale alert. Settings configures the single instance origin and reports the real readiness/listening checklist; the trigger pad keeps its 1200ms hold, and time helpers format the deadline and last-seen values.

src/lib/time.ts

@@ -40,6 +40,34 @@ export function relativeSince(value: string | null | undefined, now: number): st
   return date ? relativeTime(date, now) : null;
 }
 
+/**
+ * Time left before an alert self-destructs, e.g. `Ends in 6d 4h` / `Ends in
+ * 12m`. Null when there is no deadline or it cannot be parsed; a deadline in
+ * the past renders `Ended` (the service will 404 from then on).
+ */
+export function remainingLifetime(expiresAt: string | null | undefined, now: number): string | null {
+  const date = parseServerTime(expiresAt);
+  if (!date) return null;
+  const left = date.getTime() - now;
+  if (left <= 0) return 'Ended';
+  if (left < MINUTE) return 'Ends in under a minute';
+  if (left < HOUR) return `Ends in ${Math.floor(left / MINUTE)}m`;
+  if (left < DAY) {
+    const hours = Math.floor(left / HOUR);
+    const minutes = Math.floor((left % HOUR) / MINUTE);
+    return minutes ? `Ends in ${hours}h ${minutes}m` : `Ends in ${hours}h`;
+  }
+  const days = Math.floor(left / DAY);
+  const hours = Math.floor((left % DAY) / HOUR);
+  return hours ? `Ends in ${days}d ${hours}h` : `Ends in ${days}d`;
+}
+
+/** True when the deadline is present and already past. */
+export function isPastDeadline(expiresAt: string | null | undefined, now: number): boolean {
+  const date = parseServerTime(expiresAt);
+  return !!date && date.getTime() <= now;
+}
+
 /** Local wall-clock time for the accessibility label of a relative stamp. */
 export function absoluteLocal(date: Date): string {
   const hh = String(date.getHours()).padStart(2, '0');