Add avatar-menu navigation style and inline Android search bar

- New Settings > Appearance > "Navigation menu" toggle
  (SettingsController.navMenuStyle, NooNavMenuStyle.drawer/avatarMenu):
  the hamburger-opens-a-Drawer pattern stays the default, or the avatar
  button opens a full-width dropdown (showAvatarMenu) instead, holding
  the same hidden-tabs + Settings content the drawer does. Removes one
  of the two top-corner targets the shell asks a thumb to reach, with
  no permanent chrome added.
- NooTopBar gains androidTitleReplacement so Android's top bar can swap
  its title for an inline search-field-styled launcher
  (ShellSearchLauncher) when search isn't in the bottom bar, instead of
  a bare search icon beside it.
- ShellAvatarButton's onTap/label are now overridable so AppTopBar can
  repoint it per the new setting without this file depending on
  avatar_menu.dart (which already depends on it for shared helpers).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

lib/widgets/settings/settings_appearance.dart

@@ -51,6 +51,7 @@ class SettingsAppearanceSection extends StatelessWidget {
           children: [
             _ThemeRow(settings: settings),
             _BottomBarStyleRow(settings: settings),
+            _NavMenuStyleRow(settings: settings),
             NooSettingsRow(
               icon: LucideIcons.search,
               label: const Text('Search in bottom bar'),
@@ -230,6 +231,66 @@ class _BottomBarStyleRow extends StatelessWidget {
   }
 }
 
+/// "Navigation menu" (Settings → Appearance): which widget opens hidden
+/// tabs + Settings - the original `menu` icon that opens a left `Drawer`,
+/// or the avatar button instead (opens `showAvatarMenu`, a dropdown
+/// anchored under it) - see [NooNavMenuStyle]'s own doc comment for the
+/// full reachability rationale (dropping the hamburger removes one of the
+/// two top-corner targets the shell asks a thumb to reach, rather than
+/// adding a third kind of chrome like a side rail would).
+class _NavMenuStyleRow extends StatelessWidget {
+  final SettingsController settings;
+
+  const _NavMenuStyleRow({required this.settings});
+
+  @override
+  Widget build(BuildContext context) {
+    final colors = context.nooColors;
+    return Material(
+      color: colors.surface,
+      child: Padding(
+        padding: const EdgeInsets.symmetric(
+          horizontal: NooSpace.md,
+          vertical: 12,
+        ),
+        child: Column(
+          crossAxisAlignment: CrossAxisAlignment.start,
+          children: [
+            Row(
+              children: [
+                Icon(LucideIcons.panelLeft, size: 20, color: colors.fg2),
+                const SizedBox(width: 14),
+                Text(
+                  'Navigation menu',
+                  style: NooText.bodyL.copyWith(color: colors.fg1),
+                ),
+              ],
+            ),
+            const SizedBox(height: 12),
+            NooSegmentedControl<NooNavMenuStyle>(
+              fill: true,
+              value: settings.navMenuStyle,
+              onChanged: settings.setNavMenuStyle,
+              options: const [
+                NooSegmentOption(
+                  value: NooNavMenuStyle.drawer,
+                  icon: LucideIcons.menu,
+                  label: 'Hamburger',
+                ),
+                NooSegmentOption(
+                  value: NooNavMenuStyle.avatarMenu,
+                  icon: LucideIcons.userRound,
+                  label: 'Avatar',
+                ),
+              ],
+            ),
+          ],
+        ),
+      ),
+    );
+  }
+}
+
 /// The current accent-color choice, shown as a small filled circle in the
 /// "Accent color" row - a wallpaper icon when following the OS's dynamic
 /// color instead of a fixed swatch.