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.

lib/screens/discover_screen.dart

@@ -22,6 +22,7 @@ import '../utils/content_utils.dart';
 import '../widgets/cycling_media_backdrop.dart';
 import '../widgets/optimized_media_image.dart' show ClearLogoImage, blurArtwork;
 import '../widgets/toolbar_scrim.dart';
+import '../widgets/system_clock.dart';
 import '../providers/discover_provider.dart';
 import '../providers/multi_server_provider.dart';
 import '../providers/watch_state_store.dart';
@@ -748,6 +749,14 @@ class _DiscoverScreenState extends State<DiscoverScreen>
               style: Theme.of(context).textTheme.titleLarge?.copyWith(color: foregroundColor, fontWeight: .bold),
             ),
           const Spacer(),
+          // TV only: a fullscreen leanback app hides the system clock, while a
+          // phone status bar and a desktop menu bar already show one.
+          if (PlatformDetector.isTV()) ...[
+            SystemClock(
+              style: Theme.of(context).textTheme.titleMedium?.copyWith(color: foregroundColor, fontWeight: .w500),
+            ),
+            const SizedBox(width: 12),
+          ],
           Consumer2<WatchTogetherProvider, CompanionRemoteProvider>(
             builder: (context, watchTogether, companionRemote, _) {
               final isDesktop = PlatformDetector.shouldActAsRemoteHost(context);

lib/widgets/system_clock.dart

@@ -0,0 +1,79 @@
+import 'dart:async';
+
+import 'package:flutter/material.dart';
+
+import '../utils/formatters.dart';
+
+/// Live wall-clock label that follows the system 12/24-hour preference.
+///
+/// The displayed value comes from [formatClockTime] with
+/// `MediaQuery.alwaysUse24HourFormatOf`, so it matches the format every other
+/// time-of-day label in the app uses and flips as soon as the OS setting does.
+///
+/// Ticking is a one-shot timer re-armed onto each wall-clock minute boundary
+/// rather than a one-second poll: one rebuild per minute, and the minute never
+/// flips a fraction of a second late. A suspended process runs no timers, so
+/// the clock also resynchronises on resume instead of waiting out the boundary
+/// that elapsed while it was away.
+class SystemClock extends StatefulWidget {
+  const SystemClock({super.key, this.style, this.now = DateTime.now});
+
+  /// Text style for the clock label. The two chrome surfaces that host it use
+  /// different foregrounds, so the caller owns colour and size.
+  final TextStyle? style;
+
+  /// Wall-clock source. Overridden only by tests, which need the minute
+  /// rollover to be deterministic.
+  final DateTime Function() now;
+
+  @override
+  State<SystemClock> createState() => _SystemClockState();
+}
+
+class _SystemClockState extends State<SystemClock> with WidgetsBindingObserver {
+  Timer? _tick;
+  late DateTime _now;
+
+  @override
+  void initState() {
+    super.initState();
+    WidgetsBinding.instance.addObserver(this);
+    _now = widget.now();
+    _scheduleTick();
+  }
+
+  @override
+  void dispose() {
+    _tick?.cancel();
+    WidgetsBinding.instance.removeObserver(this);
+    super.dispose();
+  }
+
+  @override
+  void didChangeAppLifecycleState(AppLifecycleState state) {
+    if (state == AppLifecycleState.resumed) _tickNow();
+  }
+
+  void _scheduleTick() {
+    final now = _now;
+    final nextMinute = DateTime(now.year, now.month, now.day, now.hour, now.minute).add(const Duration(minutes: 1));
+    _tick?.cancel();
+    _tick = Timer(nextMinute.difference(now), _tickNow);
+  }
+
+  void _tickNow() {
+    if (!mounted) return;
+    setState(() => _now = widget.now());
+    _scheduleTick();
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return Text(
+      formatClockTime(_now, is24Hour: MediaQuery.alwaysUse24HourFormatOf(context)),
+      style: widget.style,
+      maxLines: 1,
+      softWrap: false,
+    );
+  }
+}

lib/widgets/video_controls/widgets/video_controls_header.dart

@@ -7,6 +7,7 @@ import '../../../i18n/strings.g.dart';
 import '../../../watch_together/widgets/watch_together_overlay.dart';
 import '../../../watch_together/providers/watch_together_provider.dart';
 import '../../app_bar_back_button.dart';
+import '../../system_clock.dart';
 
 /// Header layout style for video controls
 enum VideoHeaderStyle {
@@ -68,6 +69,12 @@ class VideoControlsHeader extends StatelessWidget {
             );
           },
         ),
+        Padding(
+          padding: const EdgeInsets.only(right: 8),
+          child: SystemClock(
+            style: const TextStyle(color: Colors.white70, fontSize: 14, fontWeight: .w500),
+          ),
+        ),
         ?trailing,
       ],
     );