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>

tests/web/test_next_sync_display.py

@@ -0,0 +1,36 @@
+from datetime import datetime, timezone
+
+from fastapi.testclient import TestClient
+
+
+class _FakeScheduler:
+    def __init__(self, next_tick=None) -> None:
+        self.last_tick = None
+        self.next_tick = next_tick
+
+
+def test_login_page_shows_next_sync_time(app, client: TestClient) -> None:
+    next_tick = datetime(2026, 8, 16, 14, 32, tzinfo=timezone.utc)
+    app.state.scheduler = _FakeScheduler(next_tick=next_tick)
+
+    response = client.get("/login")
+
+    assert response.status_code == 200
+    assert 'data-utc="2026-08-16T14:32:00+00:00"' in response.text
+
+
+def test_dashboard_shows_next_sync_time(app, authenticated_client) -> None:
+    next_tick = datetime(2026, 8, 16, 15, 0, tzinfo=timezone.utc)
+    app.state.scheduler = _FakeScheduler(next_tick=next_tick)
+
+    response = authenticated_client.get("/")
+
+    assert response.status_code == 200
+    assert 'data-utc="2026-08-16T15:00:00+00:00"' in response.text
+
+
+def test_login_page_renders_without_scheduler(client: TestClient) -> None:
+    response = client.get("/login")
+
+    assert response.status_code == 200
+    assert "data-utc" not in response.text