refactor(ui): share android keyboard-mode system-back guard

lib/focus/input_mode_tracker.dart

@@ -1,3 +1,5 @@
+import 'dart:io';
+
 import 'package:flutter/material.dart';
 import 'package:flutter/services.dart';
 
@@ -40,6 +42,13 @@ class InputModeTracker extends StatefulWidget {
     return of(context) == InputMode.keyboard;
   }
 
+  /// Whether system back must be blocked because the dpad key handler owns
+  /// back navigation: on Android in keyboard mode (TV/gamepad), letting the
+  /// system back through as well double-pops the route.
+  static bool shouldBlockSystemBack(BuildContext context) {
+    return Platform.isAndroid && isKeyboardMode(context);
+  }
+
   @override
   State<InputModeTracker> createState() => _InputModeTrackerState();
 }

lib/screens/media_detail_screen.dart

@@ -2999,7 +2999,7 @@ class _MediaDetailScreenState extends State<MediaDetailScreen>
           body: const Center(child: CircularProgressIndicator()),
         ),
       );
-      final blockSystemBack = Platform.isAndroid && InputModeTracker.isKeyboardMode(context);
+      final blockSystemBack = InputModeTracker.shouldBlockSystemBack(context);
       if (!blockSystemBack) {
         return loading;
       }
@@ -3021,7 +3021,7 @@ class _MediaDetailScreenState extends State<MediaDetailScreen>
 
     _scheduleInitialMobileDetailFocus(metadata);
 
-    final blockSystemBack = Platform.isAndroid && InputModeTracker.isKeyboardMode(context);
+    final blockSystemBack = InputModeTracker.shouldBlockSystemBack(context);
     final content = PrimaryScrollController(
       controller: _scrollController,
       child: IosStatusBarTapScrollToTop(
@@ -3322,7 +3322,7 @@ class _MediaDetailScreenState extends State<MediaDetailScreen>
       ],
     );
 
-    final blockSystemBack = Platform.isAndroid && InputModeTracker.isKeyboardMode(context);
+    final blockSystemBack = InputModeTracker.shouldBlockSystemBack(context);
     final content = OverlaySheetHost(
       // blockSystemBack keeps the route from double-popping on Android keyboard/
       // TV (the key handler owns dpad back); the host also closes an open sheet.