Mark the Flutter Views as focusable by setting a tabindex value.

lib/web_ui/lib/src/engine/platform_dispatcher.dart

@@ -79,7 +79,7 @@ class EnginePlatformDispatcher extends ui.PlatformDispatcher {
     _addLocaleChangedListener();
     registerHotRestartListener(dispose);
     AppLifecycleState.instance.addListener(_setAppLifecycleState);
-    ViewFocusBinding.instance.addListener(invokeOnViewFocusChange);
+    _viewFocusBinding.init();
     domDocument.body?.prepend(accessibilityPlaceholder);
     _onViewDisposedListener = viewManager.onViewDisposed.listen((_) {
       // Send a metrics changed event to the framework when a view is disposed.
@@ -123,7 +123,7 @@ class EnginePlatformDispatcher extends ui.PlatformDispatcher {
     _removeLocaleChangedListener();
     HighContrastSupport.instance.removeListener(_updateHighContrast);
     AppLifecycleState.instance.removeListener(_setAppLifecycleState);
-    ViewFocusBinding.instance.removeListener(invokeOnViewFocusChange);
+    _viewFocusBinding.dispose();
     accessibilityPlaceholder.remove();
     _onViewDisposedListener.cancel();
     viewManager.dispose();
@@ -228,6 +228,9 @@ class EnginePlatformDispatcher extends ui.PlatformDispatcher {
     }
   }
 
+  late final ViewFocusBinding _viewFocusBinding =
+    ViewFocusBinding(viewManager, invokeOnViewFocusChange);
+
   @override
   ui.ViewFocusChangeCallback? get onViewFocusChange => _onViewFocusChange;
   ui.ViewFocusChangeCallback? _onViewFocusChange;
@@ -248,7 +251,6 @@ class EnginePlatformDispatcher extends ui.PlatformDispatcher {
     );
   }
 
-
   @override
   void requestViewFocusChange({
     required int viewId,
@@ -258,7 +260,6 @@ class EnginePlatformDispatcher extends ui.PlatformDispatcher {
     // TODO(tugorez): implement this method. At the moment will be a no op call.
   }
 
-
   /// A set of views which have rendered in the current `onBeginFrame` or
   /// `onDrawFrame` scope.
   Set<ui.FlutterView>? _viewsRenderedInCurrentFrame;

lib/web_ui/lib/src/engine/platform_dispatcher/view_focus_binding.dart

@@ -2,47 +2,36 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
+import 'dart:async';
 import 'package:ui/src/engine.dart';
 import 'package:ui/ui.dart' as ui;
 
 /// Tracks the [FlutterView]s focus changes.
 final class ViewFocusBinding {
-  /// Creates a [ViewFocusBinding] instance.
-  ViewFocusBinding._();
+  ViewFocusBinding(this._viewManager, this._onViewFocusChange);
 
-  /// The [ViewFocusBinding] singleton.
-  static final ViewFocusBinding instance = ViewFocusBinding._();
+  final FlutterViewManager _viewManager;
+  final ui.ViewFocusChangeCallback _onViewFocusChange;
 
-  final List<ui.ViewFocusChangeCallback> _listeners = <ui.ViewFocusChangeCallback>[];
   int? _lastViewId;
   ui.ViewFocusDirection _viewFocusDirection = ui.ViewFocusDirection.forward;
 
-  /// Subscribes the [listener] to [ui.ViewFocusEvent] events.
-  void addListener(ui.ViewFocusChangeCallback listener) {
-    if (_listeners.isEmpty) {
-      domDocument.body?.addEventListener(_keyDown, _handleKeyDown);
-      domDocument.body?.addEventListener(_keyUp, _handleKeyUp);
-      domDocument.body?.addEventListener(_focusin, _handleFocusin);
-      domDocument.body?.addEventListener(_focusout, _handleFocusout);
-    }
-    _listeners.add(listener);
-  }
+  StreamSubscription<int>? _onViewCreatedListener;
 
-  /// Removes the [listener] from the [ui.ViewFocusEvent] events subscription.
-  void removeListener(ui.ViewFocusChangeCallback listener) {
-    _listeners.remove(listener);
-    if (_listeners.isEmpty) {
-      domDocument.body?.removeEventListener(_keyDown, _handleKeyDown);
-      domDocument.body?.removeEventListener(_keyUp, _handleKeyUp);
-      domDocument.body?.removeEventListener(_focusin, _handleFocusin);
-      domDocument.body?.removeEventListener(_focusout, _handleFocusout);
-    }
+  void init() {
+    domDocument.body?.addEventListener(_keyDown, _handleKeyDown);
+    domDocument.body?.addEventListener(_keyUp, _handleKeyUp);
+    domDocument.body?.addEventListener(_focusin, _handleFocusin);
+    domDocument.body?.addEventListener(_focusout, _handleFocusout);
+    _onViewCreatedListener = _viewManager.onViewCreated.listen(_handleViewCreated);
   }
 
-  void _notify(ui.ViewFocusEvent event) {
-    for (final ui.ViewFocusChangeCallback listener in _listeners) {
-      listener(event);
-    }
+  void dispose() {
+    domDocument.body?.removeEventListener(_keyDown, _handleKeyDown);
+    domDocument.body?.removeEventListener(_keyUp, _handleKeyUp);
+    domDocument.body?.removeEventListener(_focusin, _handleFocusin);
+    domDocument.body?.removeEventListener(_focusout, _handleFocusout);
+    _onViewCreatedListener?.cancel();
   }
 
   late final DomEventListener _handleFocusin = createDomEventListener((DomEvent event) {
@@ -71,6 +60,7 @@ final class ViewFocusBinding {
     if (viewId == _lastViewId) {
       return;
     }
+
     final ui.ViewFocusEvent event;
     if (viewId == null) {
       event = ui.ViewFocusEvent(
@@ -85,18 +75,44 @@ final class ViewFocusBinding {
         direction: _viewFocusDirection,
       );
     }
+    _maybeMarkViewAsFocusable(_lastViewId, reachableByKeyboard: true);
+    _maybeMarkViewAsFocusable(viewId, reachableByKeyboard: false);
     _lastViewId = viewId;
-    _notify(event);
+    _onViewFocusChange(event);
+  }
+
+  int? _viewId(DomElement? element) {
+    final DomElement? rootElement = element?.closest(DomManager.flutterViewTagName);
+    if (rootElement == null) {
+      return null;
+    }
+    return _viewManager.viewIdForRootElement(rootElement);
   }
 
-  static int? _viewId(DomElement? element) {
-    final DomElement? viewElement = element?.closest(
-      DomManager.flutterViewTagName,
-    );
-    final String? viewIdAttribute = viewElement?.getAttribute(
-      GlobalHtmlAttributes.flutterViewIdAttributeName,
-    );
-    return viewIdAttribute == null ? null : int.tryParse(viewIdAttribute);
+  void _handleViewCreated(int viewId) {
+    _maybeMarkViewAsFocusable(viewId, reachableByKeyboard: true);
+  }
+
+  void _maybeMarkViewAsFocusable(
+    int? viewId, {
+    required bool reachableByKeyboard,
+  }) {
+    if (viewId == null) {
+      return;
+    }
+
+    final DomElement? rootElement = _viewManager[viewId]?.dom.rootElement;
+    if (EngineSemantics.instance.semanticsEnabled) {
+      rootElement?.removeAttribute('tabindex');
+    } else {
+      // A tabindex with value zero means the DOM element can be reached by using
+      // the keyboard (tab, shift + tab). When its value is -1 it is still focusable
+      // but can't be focused by the result of keyboard events This is specially
+      // important when the semantics tree is enabled as it puts DOM nodes inside
+      // the flutter view and having it with a zero tabindex messes the focus
+      // traversal order when pressing tab or shift tab.
+      rootElement?.setAttribute('tabindex', reachableByKeyboard ? 0 : -1);
+    }
   }
 
   static const String _focusin = 'focusin';

lib/web_ui/lib/src/engine/view_embedder/flutter_view_manager.dart

@@ -96,6 +96,16 @@ class FlutterViewManager {
     return _jsViewOptions[viewId];
   }
 
+  /// Returns the [viewId] if [rootElement] corresponds to any of the [views].
+  int? viewIdForRootElement(DomElement rootElement)  {
+    for(final EngineFlutterView view in views) {
+      if (view.dom.rootElement == rootElement) {
+        return view.viewId;
+      }
+    }
+    return null;
+  }
+
   void dispose() {
     // We need to call `toList()` in order to avoid concurrent modification
     // inside the loop.

lib/web_ui/lib/src/engine/view_embedder/style_manager.dart

@@ -116,6 +116,11 @@ void applyGlobalCssRulesToSheet(
     // Hide placeholder text
     '$cssSelectorPrefix .flt-text-editing::placeholder {'
     '  opacity: 0;'
+    '}'
+
+    // Hide outline when the flutter-view root element is focused.
+    '$cssSelectorPrefix:focus {'
+    ' outline: none;'
     '}',
   );