Fix missing root Scaffold check in ScaffoldMessenger (#77410)

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

@@ -278,7 +278,7 @@ class ScaffoldMessengerState extends State<ScaffoldMessenger> with TickerProvide
 
   void _register(ScaffoldState scaffold) {
     _scaffolds.add(scaffold);
-    if (_snackBars.isNotEmpty) {
+    if (_snackBars.isNotEmpty && _isRoot(scaffold)) {
       scaffold._updateSnackBar();
     }
   }

packages/flutter/test/material/scaffold_test.dart

@@ -2199,6 +2199,77 @@ void main() {
       '   MaterialApp at the top of your application widget tree.\n'
     ));
   });
+
+  testWidgets('ScaffoldMessenger checks for nesting when a new Scaffold is registered', (WidgetTester tester) async {
+    // Regression test for https://github.com/flutter/flutter/issues/77251
+    const String snackBarContent = 'SnackBar Content';
+    await tester.pumpWidget(MaterialApp(
+      home: Builder(
+        builder: (BuildContext context) => Scaffold(
+          body: Scaffold(
+            body: TextButton(
+              onPressed: () {
+                Navigator.push(
+                  context,
+                  MaterialPageRoute<void>(
+                    builder: (BuildContext context) {
+                      return Scaffold(
+                        body: Column(
+                          children: <Widget>[
+                            TextButton(
+                              onPressed: () {
+                                const SnackBar snackBar = SnackBar(
+                                  content: Text(snackBarContent),
+                                  behavior: SnackBarBehavior.floating,
+                                );
+                                ScaffoldMessenger.of(context).showSnackBar(snackBar);
+                              },
+                              child: const Text('Show SnackBar'),
+                            ),
+                            TextButton(
+                              onPressed: () {
+                                Navigator.pop(context, null);
+                              },
+                              child: const Text('Pop route'),
+                            )
+                          ],
+                        ),
+                      );
+                    },
+                  ),
+                );
+              },
+              child: const Text('Push route'),
+            ),
+          ),
+        ),
+      )
+    ));
+
+    expect(find.text(snackBarContent), findsNothing);
+    await tester.tap(find.text('Push route'));
+    await tester.pumpAndSettle();
+    expect(find.text(snackBarContent), findsNothing);
+    expect(find.text('Pop route'), findsOneWidget);
+
+    // Show SnackBar on second page
+    await tester.tap(find.text('Show SnackBar'));
+    await tester.pump();
+    expect(find.text(snackBarContent), findsOneWidget);
+    // Pop the second page, the SnackBar completes a hero animation to the next route.
+    // If we have not handled the nested Scaffolds properly, this will throw an
+    // exception as duplicate SnackBars on the first route would have a common hero tag.
+    await tester.tap(find.text('Pop route'));
+    await tester.pump();
+    // There are SnackBars two during the execution of the hero animation.
+    expect(find.text(snackBarContent), findsNWidgets(2));
+    await tester.pumpAndSettle();
+    expect(find.text(snackBarContent), findsOneWidget);
+    // Allow the SnackBar to animate out
+    await tester.pump(const Duration(seconds: 4));
+    await tester.pumpAndSettle();
+    expect(find.text(snackBarContent), findsNothing);
+  });
 }
 
 class _GeometryListener extends StatefulWidget {