feat(ui): show a system-format clock on TV home and in the player

The clock renders through the existing formatClockTime helper driven by
MediaQuery.alwaysUse24HourFormatOf, so it follows the OS 12/24-hour
setting instead of introducing an app preference. It re-arms a one-shot
timer onto each wall-clock minute boundary rather than polling, and
resyncs on resume because a suspended process runs no timers.

The player header is shared by the mobile and desktop/TV controls, so one
insertion point covers every form factor: the player is fullscreen
everywhere, so it never has an OS clock to defer to. Home is the
exception and only gets one on TV, where a leanback app hides the system
clock; a phone status bar and a desktop menu bar already show the time.

test/widgets/system_clock_test.dart

@@ -0,0 +1,84 @@
+import 'package:flutter/material.dart';
+import 'package:flutter_test/flutter_test.dart';
+import 'package:intl/date_symbol_data_local.dart';
+import 'package:plezy/i18n/strings.g.dart';
+import 'package:plezy/widgets/system_clock.dart';
+
+void main() {
+  TestWidgetsFlutterBinding.ensureInitialized();
+
+  setUpAll(() async {
+    LocaleSettings.setLocaleSync(AppLocale.en);
+    await initializeDateFormatting('en');
+  });
+
+  testWidgets('renders 24-hour time when the system asks for it', (tester) async {
+    await _pumpClock(tester, now: () => DateTime(2026, 8, 8, 18, 5), use24Hour: true);
+
+    expect(find.text('18:05'), findsOneWidget);
+  });
+
+  testWidgets('renders 12-hour time when the system asks for it', (tester) async {
+    await _pumpClock(tester, now: () => DateTime(2026, 8, 8, 18, 5), use24Hour: false);
+
+    // CLDR separates the day period with a narrow no-break space, so match the
+    // shape rather than pinning the separator codepoint.
+    expect(_clockText(tester), matches(RegExp(r'^6:05\s?PM$')));
+  });
+
+  testWidgets('follows the system format flipping while mounted', (tester) async {
+    DateTime now() => DateTime(2026, 8, 8, 18, 5);
+    await _pumpClock(tester, now: now, use24Hour: false);
+    expect(_clockText(tester), matches(RegExp(r'^6:05\s?PM$')));
+
+    await _pumpClock(tester, now: now, use24Hour: true);
+
+    expect(_clockText(tester), '18:05');
+  });
+
+  testWidgets('advances when the wall clock crosses a minute boundary', (tester) async {
+    var now = DateTime(2026, 8, 8, 18, 5, 30);
+    await _pumpClock(tester, now: () => now, use24Hour: true);
+    expect(find.text('18:05'), findsOneWidget);
+
+    // Nothing scheduled before the boundary: the label is still the old minute
+    // 29 seconds later.
+    now = DateTime(2026, 8, 8, 18, 5, 59);
+    await tester.pump(const Duration(seconds: 29));
+    expect(find.text('18:05'), findsOneWidget);
+
+    now = DateTime(2026, 8, 8, 18, 6, 0);
+    await tester.pump(const Duration(seconds: 1));
+    expect(find.text('18:06'), findsOneWidget);
+
+    // And it re-arms rather than firing once.
+    now = DateTime(2026, 8, 8, 18, 7, 0);
+    await tester.pump(const Duration(minutes: 1));
+    expect(find.text('18:07'), findsOneWidget);
+  });
+
+  testWidgets('stops ticking once it leaves the tree', (tester) async {
+    await _pumpClock(tester, now: () => DateTime(2026, 8, 8, 18, 5), use24Hour: true);
+
+    await tester.pumpWidget(const SizedBox.shrink());
+
+    // A surviving timer would trip the binding's pending-timer invariant.
+    await tester.pump(const Duration(minutes: 5));
+    expect(find.byType(SystemClock), findsNothing);
+  });
+}
+
+Future<void> _pumpClock(WidgetTester tester, {required DateTime Function() now, required bool use24Hour}) {
+  return tester.pumpWidget(
+    MediaQuery(
+      data: MediaQueryData(alwaysUse24HourFormat: use24Hour),
+      child: Directionality(
+        textDirection: TextDirection.ltr,
+        child: SystemClock(now: now),
+      ),
+    ),
+  );
+}
+
+String _clockText(WidgetTester tester) =>
+    tester.widget<Text>(find.descendant(of: find.byType(SystemClock), matching: find.byType(Text))).data!;

test/widgets/video_controls_header_test.dart

@@ -1,5 +1,6 @@
 import 'package:flutter/material.dart';
 import 'package:flutter_test/flutter_test.dart';
+import 'package:intl/date_symbol_data_local.dart';
 import 'package:plezy/i18n/strings.g.dart';
 import 'package:plezy/media/ids.dart';
 import 'package:plezy/media/media_item.dart';
@@ -11,7 +12,10 @@ import 'package:provider/provider.dart';
 void main() {
   TestWidgetsFlutterBinding.ensureInitialized();
 
-  setUpAll(() => LocaleSettings.setLocaleSync(AppLocale.en));
+  setUpAll(() async {
+    LocaleSettings.setLocaleSync(AppLocale.en);
+    await initializeDateFormatting('en');
+  });
 
   testWidgets('title-less mapped movie builds with localized fallback in both layouts', (tester) async {
     final item = _mappedItem({'Id': 'movie-without-name', 'Type': 'Movie'});