feat(train): where sync stands in Settings, with Sync now, and the cog's dot

As Learn's and Todo's: halkyon_app's Sync card first in Settings, and the
dot on the cog while sync fails; the person's SyncService is now part of
TrainPerson, which was the only reason Train had neither (the developer's
review of 3 Nov 2026).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

apps/train/halkyon_train_flutter/lib/src/app/train_app.dart

@@ -106,6 +106,12 @@ class _TrainPersonAppState() extends State<TrainPersonApp> {
             create: (context) =>
                 OperatingCubit(AppScope.of(context).instanceOperators),
           ),
+          // Where sync stands: Settings' card and the dot on the cog, as
+          // Learn's and Todo's.
+          BlocProvider(
+            create: (context) =>
+                SyncStatusBloc(PersonScope.of<TrainPerson>(context).sync),
+          ),
           BlocProvider(
             create: (context) {
               final train = PersonScope.of<TrainPerson>(context);

apps/train/halkyon_train_flutter/lib/src/app/train_dependencies.dart

@@ -75,6 +75,10 @@ class TrainPerson(
   /// Whose they are.
   final SignedIn person, {
 
+  /// What sends their changes and brings their other devices' (D14):
+  /// Settings' Sync card and the cog's dot follow it.
+  required final SyncService sync,
+
   /// Their workouts, sealed and synced.
   required final WorkoutRepository workouts,
 
@@ -496,6 +500,7 @@ Future<TrainPerson> _openPersonData(
       : AppLifecycleListener(onResume: () => unawaited(keptMusic.sync()));
   return TrainPerson(
     person,
+    sync: sync,
     workouts: workouts,
     profile: profile,
     days: days,

apps/train/halkyon_train_flutter/lib/src/settings/settings_screen.dart

@@ -20,13 +20,16 @@ class const SettingsButton({super.key}) extends StatelessWidget {
   @override
   Widget build(BuildContext context) => IconButton(
     tooltip: AppLocalizations.of(context).settingsTitle,
-    icon: const WaitingAccountsBadge(child: Icon(LucideIcons.settings)),
+    // The dot of a failing sync, which the Sync card explains, as Learn's.
+    icon: const SyncTroubleBadge(
+      child: WaitingAccountsBadge(child: Icon(LucideIcons.settings)),
+    ),
     onPressed: () => context.push(TrainPaths.settings),
   );
 }
 
 /// Settings, over the tabs (ADR 0030, D60), grouped in cards as Learn's:
-/// the operator's card for whoever operates the instance; the training's
+/// where sync stands, with Sync now; the operator's card for whoever operates the instance; the training's
 /// screens (the body's figures, Health Connect, the Polar Loop, music,
 /// those the device has); the account, near the foot (halkyon_app's
 /// sections: whose it is on which instance, switching, signing out and
@@ -63,6 +66,10 @@ class const SettingsScreen({super.key}) extends StatelessWidget {
               child: Column(
                 crossAxisAlignment: CrossAxisAlignment.stretch,
                 children: [
+                  // Where sync stands, first, as Learn's and Todo's: the
+                  // cog's dot leads here.
+                  const SyncStatusCard(),
+                  const SizedBox(height: 12),
                   // Accounts waiting for approval, for whoever operates
                   // the instance alone (Halkyon Learn's ADR 0021, D34),
                   // first, as the cog's count leads here.