Cleans up appbar imply leading logic (#125315)

fixes https://github.com/flutter/flutter/issues/80256

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

@@ -827,7 +827,6 @@ class _AppBarState extends State<AppBar> {
 
     final bool hasDrawer = scaffold?.hasDrawer ?? false;
     final bool hasEndDrawer = scaffold?.hasEndDrawer ?? false;
-    final bool canPop = parentRoute?.canPop ?? false;
     final bool useCloseButton = parentRoute is PageRoute<dynamic> && parentRoute.fullscreenDialog;
 
     final double toolbarHeight = widget.toolbarHeight ?? appBarTheme.toolbarHeight ?? kToolbarHeight;
@@ -897,10 +896,7 @@ class _AppBarState extends State<AppBar> {
         leading = DrawerButton(
           style: IconButton.styleFrom(iconSize: overallIconTheme.size ?? 24),
         );
-        // TODO(chunhtai): remove (!hasEndDrawer && canPop) once internal tests
-        // are migrated.
-        // https://github.com/flutter/flutter/issues/80256.
-      } else if ((!hasEndDrawer && canPop) || (parentRoute?.impliesAppBarDismissal ?? false)) {
+      } else if (parentRoute?.impliesAppBarDismissal ?? false) {
         leading = useCloseButton ? const CloseButton() : const BackButton();
       }
     }

packages/flutter/test/material/app_bar_test.dart

@@ -3946,6 +3946,33 @@ void main() {
     );
   });
 
+  testWidgets('Only local entries that imply app bar dismissal will introduce an back button', (WidgetTester tester) async {
+    final GlobalKey key = GlobalKey();
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Scaffold(
+          key: key,
+          appBar: AppBar(),
+        ),
+      ),
+    );
+    expect(find.byType(BackButton), findsNothing);
+
+    // Push one entry that doesn't imply app bar dismissal.
+    ModalRoute.of(key.currentContext!)!.addLocalHistoryEntry(
+      LocalHistoryEntry(onRemove: () {}, impliesAppBarDismissal: false),
+    );
+    await tester.pump();
+    expect(find.byType(BackButton), findsNothing);
+
+    // Push one entry that implies app bar dismissal.
+    ModalRoute.of(key.currentContext!)!.addLocalHistoryEntry(
+      LocalHistoryEntry(onRemove: () {}),
+    );
+    await tester.pump();
+    expect(find.byType(BackButton), findsOneWidget);
+  });
+
   testWidgets('AppBar.preferredHeightFor', (WidgetTester tester) async {
     late double preferredHeight;
     late Size preferredSize;