Turn the next-sync indicator into a live ticking countdown

Replaces the one-time UTC-to-local formatting with a per-second
countdown (HH:MM:SS, or MM:SS under an hour) that fits the dark
cockpit theme's instrument-panel feel, falling back to "due now" once
the target passes instead of showing a negative duration.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

app/web/static/app.js

@@ -1,10 +1,39 @@
-document.addEventListener("DOMContentLoaded", () => {
-    document.querySelectorAll("time[data-utc]").forEach((el) => {
-        const date = new Date(el.dataset.utc);
-        if (Number.isNaN(date.getTime())) {
-            return;
+function formatCountdown(remainingMs) {
+    if (remainingMs <= 0) {
+        return "due now";
+    }
+    const totalSeconds = Math.floor(remainingMs / 1000);
+    const hours = Math.floor(totalSeconds / 3600);
+    const minutes = Math.floor((totalSeconds % 3600) / 60);
+    const seconds = totalSeconds % 60;
+    const pad = (n) => String(n).padStart(2, "0");
+    if (hours > 0) {
+        return `${pad(hours)}:${pad(minutes)}:${pad(seconds)}`;
+    }
+    return `${pad(minutes)}:${pad(seconds)}`;
+}
+
+function startSyncCountdown(el) {
+    const target = new Date(el.dataset.utc);
+    if (Number.isNaN(target.getTime())) {
+        return;
+    }
+    el.title = `${target.toLocaleString(undefined, { dateStyle: "medium", timeStyle: "short" })} · ${el.dataset.utc} UTC`;
+
+    let intervalId = null;
+    const tick = () => {
+        const remaining = target.getTime() - Date.now();
+        el.textContent = formatCountdown(remaining);
+        if (remaining <= 0 && intervalId !== null) {
+            clearInterval(intervalId);
         }
-        el.textContent = date.toLocaleString(undefined, { dateStyle: "medium", timeStyle: "short" });
-        el.title = `${el.dataset.utc} (UTC)`;
-    });
+    };
+    tick();
+    if (target.getTime() - Date.now() > 0) {
+        intervalId = setInterval(tick, 1000);
+    }
+}
+
+document.addEventListener("DOMContentLoaded", () => {
+    document.querySelectorAll("time.next-sync[data-utc]").forEach(startSyncCountdown);
 });