feat(shell): the rail's logo leads Home

From medium windows on, the kingfisher atop the navigation rail is a
button to Home, as a website's logo leads to its start, with the tick the
rail's own choices make.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MMm7usAo6q9ZZRoPkWjoxi
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

halkyon_learn_flutter/lib/src/core/router/app_shell.dart

@@ -77,7 +77,7 @@ class _AppShellState() extends State<AppShell> {
             selectedIndex: navigationShell.currentIndex,
             labelType: NavigationRailLabelType.all,
             onDestinationSelected: _select,
-            leading: const _RailLogo(),
+            leading: _RailLogo(onTap: () => _select(0)),
             destinations: [
               for (final destination in destinations)
                 NavigationRailDestination(
@@ -141,26 +141,41 @@ class _AppShellState() extends State<AppShell> {
   }
 }
 
-/// The kingfisher atop the rail. The icon has a white background, so it sits
+/// The kingfisher atop the rail, leading Home ([onTap]) as a website's
-/// in a rounded tile that reads on light and dark rails alike.
+/// logo does. The icon has a white background, so it sits in a rounded tile
-class const _RailLogo() extends StatelessWidget {
+/// that reads on light and dark rails alike.
+class const _RailLogo({required final VoidCallback onTap})
+    extends StatelessWidget {
   @override
-  Widget build(BuildContext context) => Padding(
+  Widget build(BuildContext context) {
+    final l10n = AppLocalizations.of(context);
+    return Padding(
       padding: const EdgeInsets.symmetric(vertical: 12),
+      child: Tooltip(
+        message: l10n.shellTabHome,
+        child: Material(
+          type: MaterialType.transparency,
+          child: InkWell(
+            onTap: onTap,
+            borderRadius: BorderRadius.circular(9),
             child: ClipRRect(
               borderRadius: BorderRadius.circular(9),
               child: Image.asset(
                 'assets/icon/halkyon_icon.png',
                 width: 40,
                 height: 40,
-        // The source is 1024 px square; a 40 dp logo needs no more than this
+                // The source is 1024 px square; a 40 dp logo needs no more
-        // in memory, even at three times the density.
+                // than this in memory, even at three times the density.
                 cacheWidth: 120,
-        semanticLabel: AppLocalizations.of(context).appTitle,
+                semanticLabel: l10n.appTitle,
+              ),
+            ),
+          ),
         ),
       ),
     );
   }
+}
 
 /// A tab: its label and icons. Lucide's icons are outlines with few filled
 /// companions: the library switches from a closed to an open book, and the

halkyon_learn_flutter/test/core/router/app_shell_test.dart

@@ -9,6 +9,7 @@ import 'package:halkyon_learn_flutter/src/core/widget/screen_tint.dart';
 import 'package:halkyon_learn_flutter/src/core/widget/top_gradient.dart';
 import 'package:halkyon_learn_flutter/src/feature/card/data/card_repository.dart';
 import 'package:halkyon_learn_flutter/src/feature/card/model/card_content.dart';
+import 'package:halkyon_learn_flutter/src/feature/home/widget/home_screen.dart';
 import 'package:halkyon_learn_flutter/src/feature/studyset/data/studyset_payload.dart';
 import 'package:halkyon_learn_flutter/src/feature/studyset/model/studyset_content.dart';
 import 'package:halkyon_learn_flutter/src/feature/studyset/widget/studyset_screen.dart';
@@ -175,6 +176,17 @@ void main() {
     expect(find.byType(NavigationBar), findsOneWidget);
   });
 
+  testWidgets("in wider windows, the rail's logo leads Home, as a "
+      "website's does", (tester) async {
+    await showApp(tester);
+    await openJapanese(tester);
+
+    await tester.tap(find.bySemanticsLabel('Halkyon Learn'));
+    await tester.pumpAndSettle();
+
+    expect(find.byType(HomeScreen), findsOneWidget);
+  });
+
   testWidgets('in wider windows, the rail stays inside a studyset', (
     tester,
   ) async {