Show next scheduled sync time on every page

Exposes the scheduler's next_tick in the topbar via a safe Jinja
helper (falls back to nothing if the scheduler isn't running yet),
and converts the server-rendered UTC timestamp to the visitor's local
time client-side so it reads correctly regardless of timezone.

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

app/web/static/app.js

@@ -0,0 +1,10 @@
+document.addEventListener("DOMContentLoaded", () => {
+    document.querySelectorAll("time[data-utc]").forEach((el) => {
+        const date = new Date(el.dataset.utc);
+        if (Number.isNaN(date.getTime())) {
+            return;
+        }
+        el.textContent = date.toLocaleString(undefined, { dateStyle: "medium", timeStyle: "short" });
+        el.title = `${el.dataset.utc} (UTC)`;
+    });
+});

app/web/static/style.css

@@ -64,12 +64,36 @@ a:hover {
     border-radius: 7px;
 }
 
+.topbar-right {
+    display: flex;
+    align-items: center;
+    gap: 1.25rem;
+    flex-wrap: wrap;
+}
+
 .topbar nav {
     display: flex;
     gap: 1.25rem;
     font-size: 0.9rem;
 }
 
+.sync-status {
+    display: inline-flex;
+    align-items: center;
+    gap: 0.35rem;
+    padding: 0.3rem 0.7rem;
+    border-radius: 999px;
+    background: var(--info-bg);
+    color: var(--info);
+    font-size: 0.78rem;
+    font-weight: 600;
+    white-space: nowrap;
+}
+
+.sync-status time {
+    font-weight: 700;
+}
+
 .container {
     max-width: 960px;
     margin: 0 auto;