app bar leading back button should not change if the route is popped (#71944)

packages/flutter/lib/src/material/app_bar.dart

@@ -709,6 +709,8 @@ class _AppBarState extends State<AppBar> {
     Scaffold.of(context).openEndDrawer();
   }
 
+  bool? hadBackButtonWhenRouteWasActive;
+
   @override
   Widget build(BuildContext context) {
     assert(!widget.primary || debugCheckHasMediaQuery(context));
@@ -721,7 +723,11 @@ class _AppBarState extends State<AppBar> {
 
     final bool hasDrawer = scaffold?.hasDrawer ?? false;
     final bool hasEndDrawer = scaffold?.hasEndDrawer ?? false;
-    final bool canPop = parentRoute?.canPop ?? false;
+    hadBackButtonWhenRouteWasActive ??= false;
+    if (parentRoute?.isActive == true) {
+      hadBackButtonWhenRouteWasActive = parentRoute!.canPop;
+    }
+    assert(hadBackButtonWhenRouteWasActive != null);
     final bool useCloseButton = parentRoute is PageRoute<dynamic> && parentRoute.fullscreenDialog;
 
     final double toolbarHeight = widget.toolbarHeight ?? kToolbarHeight;
@@ -790,7 +796,7 @@ class _AppBarState extends State<AppBar> {
           tooltip: MaterialLocalizations.of(context).openAppDrawerTooltip,
         );
       } else {
-        if (!hasEndDrawer && canPop)
+        if (!hasEndDrawer && hadBackButtonWhenRouteWasActive!)
           leading = useCloseButton ? const CloseButton() : const BackButton();
       }
     }

packages/flutter/lib/src/widgets/routes.dart

@@ -1460,7 +1460,7 @@ abstract class ModalRoute<T> extends TransitionRoute<T> with LocalHistoryRoute<T
   /// When this changes, if the route is visible, the route will
   /// rebuild, and any widgets that used [ModalRoute.of] will be
   /// notified.
-  bool get canPop => !isFirst || willHandlePopInternally;
+  bool get canPop => isActive && (!isFirst || willHandlePopInternally);
 
   // Internals
 

packages/flutter/test/material/app_bar_test.dart

@@ -1122,6 +1122,97 @@ void main() {
     expect(find.byIcon(Icons.menu), findsNothing);
   });
 
+  testWidgets('AppBar does not update the leading if a route is popped case 1', (WidgetTester tester) async {
+    final Page<void> page1 = MaterialPage<void>(
+      key: const ValueKey<String>('1'),
+      child: Scaffold(
+        key: const ValueKey<String>('1'),
+        appBar: AppBar(),
+      )
+    );
+    final Page<void> page2 = MaterialPage<void>(
+        key: const ValueKey<String>('2'),
+        child: Scaffold(
+          key: const ValueKey<String>('2'),
+          appBar: AppBar(),
+        )
+    );
+    List<Page<void>> pages = <Page<void>>[ page1 ];
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Navigator(
+          pages: pages,
+          onPopPage: (Route<dynamic> route, dynamic result) => false,
+        ),
+      ),
+    );
+    expect(find.byType(BackButton), findsNothing);
+    // Update pages
+    pages = <Page<void>>[ page2 ];
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Navigator(
+          pages: pages,
+          onPopPage: (Route<dynamic> route, dynamic result) => false,
+        ),
+      ),
+    );
+    expect(find.byType(BackButton), findsNothing);
+  });
+
+  testWidgets('AppBar does not update the leading if a route is popped case 2', (WidgetTester tester) async {
+    final Page<void> page1 = MaterialPage<void>(
+        key: const ValueKey<String>('1'),
+        child: Scaffold(
+          key: const ValueKey<String>('1'),
+          appBar: AppBar(),
+        )
+    );
+    final Page<void> page2 = MaterialPage<void>(
+        key: const ValueKey<String>('2'),
+        child: Scaffold(
+          key: const ValueKey<String>('2'),
+          appBar: AppBar(),
+        )
+    );
+    List<Page<void>> pages = <Page<void>>[ page1, page2 ];
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Navigator(
+          pages: pages,
+          onPopPage: (Route<dynamic> route, dynamic result) => false,
+        ),
+      ),
+    );
+    // The page2 should have a back button
+    expect(
+      find.descendant(
+        of: find.byKey(const ValueKey<String>('2')),
+        matching: find.byType(BackButton),
+      ),
+      findsOneWidget
+    );
+    // Update pages
+    pages = <Page<void>>[ page1 ];
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Navigator(
+          pages: pages,
+          onPopPage: (Route<dynamic> route, dynamic result) => false,
+        ),
+      ),
+    );
+    await tester.pump(const Duration(milliseconds: 10));
+    // The back button should persist during the pop animation.
+    expect(
+      find.descendant(
+        of: find.byKey(const ValueKey<String>('2')),
+        matching: find.byType(BackButton),
+      ),
+      findsOneWidget
+    );
+  });
+
   testWidgets('AppBar ink splash draw on the correct canvas', (WidgetTester tester) async {
     // This is a regression test for https://github.com/flutter/flutter/issues/58665
     final Key key = UniqueKey();